Compacting time! Look over the section summary for section 7.1. Unless you have questions, we will assume that you've already learned this part and we will move on.
Work problem 7.38 (and 7.37 for those who missed class today).
Make progress on your book. If you need a book approved, send me an email.
Tuesday, November 17, 2009
Wednesday, November 04, 2009
Chapter 6 - Probability
Now probability wasn't so bad, was it?
Today we investigated multiple representations of categorical data: contingency tables, tree diagrams, and Venn diagrams. Each has its merits. All will provide the information you need to answer probability problems.
HW due Thursday, Nov 5: Take notes on section 5.2, pages 407-417 in the text. Work at least two problems from each of the problem sets in that section.
Standards: Section IIIA all
Concepts: Law of Large Numbers, multiplication rule, addition rule, sample space, continuous and discrete random variables, independence, expected value.
Essential questions: Why would we call the laws of probability laws? How can they be used? What does mathematical independence mean? How do we extract the important elements from a word problem so we can solve it?
Work problems from Chapter 6 in preparation for a test on Monday, November 16.
Today we investigated multiple representations of categorical data: contingency tables, tree diagrams, and Venn diagrams. Each has its merits. All will provide the information you need to answer probability problems.
HW due Thursday, Nov 5: Take notes on section 5.2, pages 407-417 in the text. Work at least two problems from each of the problem sets in that section.
Standards: Section IIIA all
Concepts: Law of Large Numbers, multiplication rule, addition rule, sample space, continuous and discrete random variables, independence, expected value.
Essential questions: Why would we call the laws of probability laws? How can they be used? What does mathematical independence mean? How do we extract the important elements from a word problem so we can solve it?
Work problems from Chapter 6 in preparation for a test on Monday, November 16.
Tuesday, October 27, 2009
Chapter 5 - Producing data
This unit covers survey design, observational studies, and experimental design. The standards involved are found under section II:
II. Sampling and Experimentation: Planning and conducting a study (10%–15%)
Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis.
A. Overview of methods of data collection
1. Census
2. Sample survey
3. Experiment
4. Observational study
B. Planning and conducting surveys
1. Characteristics of a well-designed and well-conducted survey
2. Populations, samples, and random selection
3. Sources of bias in sampling and surveys
4. Sampling methods, including simple random sampling, stratified random sampling, and cluster sampling
C. Planning and conducting experiments
1. Characteristics of a well-designed and well-conducted experiment
2. Treatments, control groups, experimental units, random assignments, and replication
3. Sources of bias and confounding, including placebo effect and blinding
4. Completely randomized design
5. Randomized block design, including matched pairs design
D. Generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys
We have looked at the mechanics used in selecting random samples using the table of random digits and simpler methods.
HW due Monday: Work as many problems from pages 371-373 as you need to be proficient with blocking and matched pairs design.
HW due Wednesday: an annotated vocabulary list from this chapter. Include explanations of why each term is good for design or a problem for design.
HW due Friday: Bring a printed copy of your electronic research proposal. We will be modifying it. You should go to the Cobb County School District website to see what the requirements are for research in our schools. Also go to the Institutional Review Board (IRB) site for the college you are most interested in and review their requirements. Be sure to answer all the questions these forms aske except for the statistical analysis questions.
II. Sampling and Experimentation: Planning and conducting a study (10%–15%)
Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis.
A. Overview of methods of data collection
1. Census
2. Sample survey
3. Experiment
4. Observational study
B. Planning and conducting surveys
1. Characteristics of a well-designed and well-conducted survey
2. Populations, samples, and random selection
3. Sources of bias in sampling and surveys
4. Sampling methods, including simple random sampling, stratified random sampling, and cluster sampling
C. Planning and conducting experiments
1. Characteristics of a well-designed and well-conducted experiment
2. Treatments, control groups, experimental units, random assignments, and replication
3. Sources of bias and confounding, including placebo effect and blinding
4. Completely randomized design
5. Randomized block design, including matched pairs design
D. Generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys
We have looked at the mechanics used in selecting random samples using the table of random digits and simpler methods.
HW due Monday: Work as many problems from pages 371-373 as you need to be proficient with blocking and matched pairs design.
HW due Wednesday: an annotated vocabulary list from this chapter. Include explanations of why each term is good for design or a problem for design.
HW due Friday: Bring a printed copy of your electronic research proposal. We will be modifying it. You should go to the Cobb County School District website to see what the requirements are for research in our schools. Also go to the Institutional Review Board (IRB) site for the college you are most interested in and review their requirements. Be sure to answer all the questions these forms aske except for the statistical analysis questions.
Thursday, October 01, 2009
Chapter 4 Non-linear relationships
Standards: I D (exploring scatterplots, transformations to achieve linearity) and E (exploring categorical data, two-way tables, etc.).
Thursday 9/24 Today we revisited residuals and the LSRL. We looked at data that appeared at first to be linear, but upon inspection were clearly not linear. That's what residuals can do for you!
We also straightened our first data set. We took exponential data--ordered pairs of the form (x, ab^x)-- and transformed them into a straightened set. Once you have straightened data, you can use the LSRL function on the calculator. We found the LSRL, converted it to a curve using our knowledge of exponents and logs, and graphed the curve through our exponential data. Ooo. Ahhh.
Procedure: Enter x and y into L1 and L2
Look at the data. See that they are not straight, but exponential in shape.
Take the ln of the y values (put in L3).
Look at scatterplot of L1, L3. Straight? Then --> LSRL
Change y-hat to ln-y-hat because we used the ln y instead of y.
Solve for y.
Graph that new equation with the original L1, L2 data.
Be proud.
September 28th: We looked at several non-linear models and discovered what transformations would make the "right" side a linear function. Those realizations drive our decisions to take logs or square roots of the original variables.
HW: problems 4.11 and 4.12 from the text.
September 29th: We worked through parts of problem 4.12 and reviewed properties and purposes of logs. Do problems 4.15 and 4.16 for Wednesday.
October 1st: Worked with transformations more today. Finished up the analysis of the disappearing dice lab where we modeled exponential decay.
Took a quiz on residuals to give students an opportunity to recoup some points from the Ch 3 test. It worked for some. Why pass up an chance to improve your grade? A copy of one version of the quiz can be found on the Typepad blog. Scroll down to Documents for AP Statistics.
October 2nd: Quizzed again today on computing, graphing, and interepreting residuals. This concept is critical to continuing in Stat. Most students have now demonstrated mastery, but those of you who have not shown me that you can do it need to step up! HW due Monday: 4.26, 4.27. 4.28 from the text. Be prepared for the next quiz on finding residuals and transforming data.
October 5th and 6th: We've been spending a lot of time perfecting our understanding and skills regarding transformations, least squares regression, and interpreting residuals. We will have nearly daily quizzes to assess our progress. In addition we are looking at contingency tables (2-way tables). We computed joint, marginal, and conditional probability and took a quick look at the meaning of independence.
HW: Read section 4.2 and do problems 4.29 and 4.30. They are pretty cool.
Thursday 9/24 Today we revisited residuals and the LSRL. We looked at data that appeared at first to be linear, but upon inspection were clearly not linear. That's what residuals can do for you!
We also straightened our first data set. We took exponential data--ordered pairs of the form (x, ab^x)-- and transformed them into a straightened set. Once you have straightened data, you can use the LSRL function on the calculator. We found the LSRL, converted it to a curve using our knowledge of exponents and logs, and graphed the curve through our exponential data. Ooo. Ahhh.
Procedure: Enter x and y into L1 and L2
Look at the data. See that they are not straight, but exponential in shape.
Take the ln of the y values (put in L3).
Look at scatterplot of L1, L3. Straight? Then --> LSRL
Change y-hat to ln-y-hat because we used the ln y instead of y.
Solve for y.
Graph that new equation with the original L1, L2 data.
Be proud.
September 28th: We looked at several non-linear models and discovered what transformations would make the "right" side a linear function. Those realizations drive our decisions to take logs or square roots of the original variables.
HW: problems 4.11 and 4.12 from the text.
September 29th: We worked through parts of problem 4.12 and reviewed properties and purposes of logs. Do problems 4.15 and 4.16 for Wednesday.
October 1st: Worked with transformations more today. Finished up the analysis of the disappearing dice lab where we modeled exponential decay.
Took a quiz on residuals to give students an opportunity to recoup some points from the Ch 3 test. It worked for some. Why pass up an chance to improve your grade? A copy of one version of the quiz can be found on the Typepad blog. Scroll down to Documents for AP Statistics.
October 2nd: Quizzed again today on computing, graphing, and interepreting residuals. This concept is critical to continuing in Stat. Most students have now demonstrated mastery, but those of you who have not shown me that you can do it need to step up! HW due Monday: 4.26, 4.27. 4.28 from the text. Be prepared for the next quiz on finding residuals and transforming data.
October 5th and 6th: We've been spending a lot of time perfecting our understanding and skills regarding transformations, least squares regression, and interpreting residuals. We will have nearly daily quizzes to assess our progress. In addition we are looking at contingency tables (2-way tables). We computed joint, marginal, and conditional probability and took a quick look at the meaning of independence.
HW: Read section 4.2 and do problems 4.29 and 4.30. They are pretty cool.
Friday, September 11, 2009
Chapter 3 Exploring Linear Relationships
No CiCi's on Sunday, September 20. Let's give the Accel Math II kids a chance.
The focus of this unit will be on standards I D 1-5 plus inference for regression (IV A 8 and IV B 7). These topics can be found in Chapters 3 and 15 of the text.
First up, we look at graphs of bivariate data. You must be able to graph (x,y) pairs on the Cartesian plane. We will be finding the Least Squares Regression Line (y-hat = a + bx) and interpreting multiple measures of fit. R is not the answer!!! You will be expected to calculate the LSRL using tables and formulas. There will be a couple of formulas that you should memorize, but now is a good time to get the green formula sheet out to see the formulas that you will be provided on all tests.
The most important formula so far is the formula for residuals: y - y-hat = the observed minus the expected [for each value of y].
Be prepared for a lab in class on Wednesday. Dress appropriately.
Friday 9/11/09: In our short period today we investigated the deviations and the residuals and just barely got to the formula that uses the squared deviations and the squared residuals:
First The deviations = the predicted differences + the residuals
Second 1 - (the sum of the squared residuals)/(the sum of the squared deviations) = r^2
Did you get that? R-squared equals the portion of the squared deviation that is not the squared error part. In other words, it is the part of the deviations that we could have predicted.
TO get these sums of the squared values we used the lists in the calculator like this:
L1: the x values
L2: the y values
Ran LinReg L1, L2, y1
L3: the predicted values of y FORUMULA= Y1(L1)
L4: the squared residuals FORMULA= (L2-L3)^2
L5: the squared deviations FORMULA= (L2-mean(L2))^2
Then use the LIST MATH 5.sum (L4) and (L5) to get the sums of the squared errors SSE and the sum of the squared deviations SST, respectively.
The R^2 formula is then 1 - (SSE/SST).
Take notes on all of Chapter 3 for Monday. Our test is Thursday.
The formulas we used in class on Monday were
b = r * Sy / Sx.
r = (sum of (Z of x * Z of y))/(n-1)
a = y-bar minus b * x-bar
HW is at least three and no more than 15 problems from the Chapter review for Chapter 3. We will cover the aspects of inference for linear regression on Tuesday.
s = the standard error about the line= an approximation of the average residual for that LSRL
SEb = the standard error of the slopes of the regression line. You would expect the slope to vary by about this much on average when you used different points from the population to come up with a LSRL.
beta = the slope of the real relationship between x and y, is approximated by b
alpha = the real y-intercept of the real relationship between x and y, approximated by a
Confidence interval for the slope : b +/- about 2 * SEb
T-statistic for testing Ho: beta = 0
b/SEb
STUDY for the test.
Test date 9/17/09.
Preview Chapter 4 for homework. See you on Monday.
The focus of this unit will be on standards I D 1-5 plus inference for regression (IV A 8 and IV B 7). These topics can be found in Chapters 3 and 15 of the text.
First up, we look at graphs of bivariate data. You must be able to graph (x,y) pairs on the Cartesian plane. We will be finding the Least Squares Regression Line (y-hat = a + bx) and interpreting multiple measures of fit. R is not the answer!!! You will be expected to calculate the LSRL using tables and formulas. There will be a couple of formulas that you should memorize, but now is a good time to get the green formula sheet out to see the formulas that you will be provided on all tests.
The most important formula so far is the formula for residuals: y - y-hat = the observed minus the expected [for each value of y].
Be prepared for a lab in class on Wednesday. Dress appropriately.
Friday 9/11/09: In our short period today we investigated the deviations and the residuals and just barely got to the formula that uses the squared deviations and the squared residuals:
First The deviations = the predicted differences + the residuals
Second 1 - (the sum of the squared residuals)/(the sum of the squared deviations) = r^2
Did you get that? R-squared equals the portion of the squared deviation that is not the squared error part. In other words, it is the part of the deviations that we could have predicted.
TO get these sums of the squared values we used the lists in the calculator like this:
L1: the x values
L2: the y values
Ran LinReg L1, L2, y1
L3: the predicted values of y FORUMULA= Y1(L1)
L4: the squared residuals FORMULA= (L2-L3)^2
L5: the squared deviations FORMULA= (L2-mean(L2))^2
Then use the LIST MATH 5.sum (L4) and (L5) to get the sums of the squared errors SSE and the sum of the squared deviations SST, respectively.
The R^2 formula is then 1 - (SSE/SST).
Take notes on all of Chapter 3 for Monday. Our test is Thursday.
The formulas we used in class on Monday were
b = r * Sy / Sx.
r = (sum of (Z of x * Z of y))/(n-1)
a = y-bar minus b * x-bar
HW is at least three and no more than 15 problems from the Chapter review for Chapter 3. We will cover the aspects of inference for linear regression on Tuesday.
s = the standard error about the line= an approximation of the average residual for that LSRL
SEb = the standard error of the slopes of the regression line. You would expect the slope to vary by about this much on average when you used different points from the population to come up with a LSRL.
beta = the slope of the real relationship between x and y, is approximated by b
alpha = the real y-intercept of the real relationship between x and y, approximated by a
Confidence interval for the slope : b +/- about 2 * SEb
T-statistic for testing Ho: beta = 0
b/SEb
STUDY for the test.
Test date 9/17/09.
Preview Chapter 4 for homework. See you on Monday.
Friday, August 28, 2009
Chapters 1 & 2
We're tying up loose ends related to interpreting visual displays of data and describing or summarizing the distributions. Our test on topics of chapters 1 and 2 will be on Thursday, September 3.
Standards: IA1-4, IB 1-2
HW due Monday: Problems 2.10, 2.12, 2.13, and 2.14. Problem 14 requires you to use your TI-83 calculator.
See you at CiCi's on Sunday from 2-4. That's near the Super WalMart at Trickum and HWY 92.
Test on Chapters 1 & 2 is Thursday. Prepare by reviewing the Chapter summaries, using a study guide, taking the online quizzes at the textbook website.
Standards: IA1-4, IB 1-2
HW due Monday: Problems 2.10, 2.12, 2.13, and 2.14. Problem 14 requires you to use your TI-83 calculator.
See you at CiCi's on Sunday from 2-4. That's near the Super WalMart at Trickum and HWY 92.
Test on Chapters 1 & 2 is Thursday. Prepare by reviewing the Chapter summaries, using a study guide, taking the online quizzes at the textbook website.
Tuesday, August 25, 2009
Welcome to the new school year
Welcome to AP Statistics.
For the first two weeks of school we will explore aspects of data collection, interpretation, and representation, topics identified by College Board in the Topics Outline for AP Statistics.
EQ: What challenges are there in collecting data? What options do we have for representing data? What changes would we make for different audiences?
8/10/09: Standards IIB 1 & 3
HW: replace the batteries in your TI-83, TI-84, or N-spire calculator, procure a bookcover to bring to class next week, and generate a lovely graph of the data you collected today.
8/11/09: See last night's homework PLUS create a graph that shows the cumulative frequency for the different responses, from most frequent to least frequent. The height of the first bar should be the frequency of the most common reponse, while the last (cumulative one) will be the size of the class.
8/12/09: Great job on the normal distribution today. Use it in good health in AP Psychology! If you haven't replaced your batteries, you still need to do that. If you haven't procured a book cover, then check into your many options. See you Thursday. Standards IC4, IIIC1
8/13/09: Today we got our textbooks and worked with the standard normal table. Do problems 2.23-2.28 from the text for homework. You will find these problems in Chapter 2 (of course!) numbered sequentially from the beginning of the chapter. There are examples and explanations in the pages leading up to these problems in the text, so use your resources wisely.
8/14/09: Does your brain still hurt? Today we explored probability density functions including the uniform, the Normal, and the triangular. When we looked at the triangular we reinforced our notions of percentiles and probability in the context of a continuous function. The standard introduced today was IB3. Your homework is problems 2.31-2.34 in the text. These are the 31st through the 34th exercises in Chapter 2.
I am not planning to start the CiCi's Sundays yet because we are still just surveying the concepts from the course. If you have questions, please see me before school on Monday. Have a super weekend. Go Lady Trojans Softball and Volleyball players! Good luck against Colquitt Co, football players! Marching band, march on with pride!
Please cover your textbook and CHANGE THOSE BATTERIES!
HW due Tuesday Aug 18th: Problems 1.7, 1.8, 1.9, and 1.11 from Chapter 1. The problems are numbered sequentially in the text, so start at the beginning and keep going until you find these problems. If you have difficulty, look at the examples on the pages prior to the problems.
HW due Wednesday Aug 19th: All the problems from the section 1.1 summary area (page 67-69) that you know how to do. I will assign additional work for each problem that you don't know how to do to get you caught up, so do your best.
HW due Thursday Aug 20th: Using the data you recorded in class today about work experience and gender, create and discuss the graph that best reflects the relationship between these two characteristics. Also, here's an interesting link about the ACT. Compare the performance of each subgroup to the national subgroup averages. Then compare the overall performance of Georgia students to the entire population of test-takers. Can you explain the difference?
HW due Monday, August 24th: Bring two different types of published graphs to class (cut out of the newspaper, magazine, or other publication or printed from the Internet PLUS enough information about the data collected that you can write up an interpretation as an expert.
HW due Tuesday, August 25th: Problems 1.39, 1.40, 1.42, and 1.43. Bring those graphs from the weekend, too!
HW due Wednesday: THe same as last night! Be sure to bring these items tomorrow. ALSO, cover your textbook.
NO CiCi's this week. Probably next!
For the first two weeks of school we will explore aspects of data collection, interpretation, and representation, topics identified by College Board in the Topics Outline for AP Statistics.
EQ: What challenges are there in collecting data? What options do we have for representing data? What changes would we make for different audiences?
8/10/09: Standards IIB 1 & 3
HW: replace the batteries in your TI-83, TI-84, or N-spire calculator, procure a bookcover to bring to class next week, and generate a lovely graph of the data you collected today.
8/11/09: See last night's homework PLUS create a graph that shows the cumulative frequency for the different responses, from most frequent to least frequent. The height of the first bar should be the frequency of the most common reponse, while the last (cumulative one) will be the size of the class.
8/12/09: Great job on the normal distribution today. Use it in good health in AP Psychology! If you haven't replaced your batteries, you still need to do that. If you haven't procured a book cover, then check into your many options. See you Thursday. Standards IC4, IIIC1
8/13/09: Today we got our textbooks and worked with the standard normal table. Do problems 2.23-2.28 from the text for homework. You will find these problems in Chapter 2 (of course!) numbered sequentially from the beginning of the chapter. There are examples and explanations in the pages leading up to these problems in the text, so use your resources wisely.
8/14/09: Does your brain still hurt? Today we explored probability density functions including the uniform, the Normal, and the triangular. When we looked at the triangular we reinforced our notions of percentiles and probability in the context of a continuous function. The standard introduced today was IB3. Your homework is problems 2.31-2.34 in the text. These are the 31st through the 34th exercises in Chapter 2.
I am not planning to start the CiCi's Sundays yet because we are still just surveying the concepts from the course. If you have questions, please see me before school on Monday. Have a super weekend. Go Lady Trojans Softball and Volleyball players! Good luck against Colquitt Co, football players! Marching band, march on with pride!
Please cover your textbook and CHANGE THOSE BATTERIES!
HW due Tuesday Aug 18th: Problems 1.7, 1.8, 1.9, and 1.11 from Chapter 1. The problems are numbered sequentially in the text, so start at the beginning and keep going until you find these problems. If you have difficulty, look at the examples on the pages prior to the problems.
HW due Wednesday Aug 19th: All the problems from the section 1.1 summary area (page 67-69) that you know how to do. I will assign additional work for each problem that you don't know how to do to get you caught up, so do your best.
HW due Thursday Aug 20th: Using the data you recorded in class today about work experience and gender, create and discuss the graph that best reflects the relationship between these two characteristics. Also, here's an interesting link about the ACT. Compare the performance of each subgroup to the national subgroup averages. Then compare the overall performance of Georgia students to the entire population of test-takers. Can you explain the difference?
HW due Monday, August 24th: Bring two different types of published graphs to class (cut out of the newspaper, magazine, or other publication or printed from the Internet PLUS enough information about the data collected that you can write up an interpretation as an expert.
HW due Tuesday, August 25th: Problems 1.39, 1.40, 1.42, and 1.43. Bring those graphs from the weekend, too!
HW due Wednesday: THe same as last night! Be sure to bring these items tomorrow. ALSO, cover your textbook.
NO CiCi's this week. Probably next!
Monday, May 04, 2009
Last few weeks
QUESTIONS FOR JUNIORS AND SOPHS:
1st - 5
2nd - 2
6th - 6
7th - 5
Answer completely and correctly. Bring it with you to the exam along with a calculator and a pencil, but no notebooks or backpacks. We need to cut down on the end-of-year littering around the school neighborhood.
Senior take-home exam assignments: Bring a perfect and complete response to the assigned question on the day of your final along with your textbook and green t-table card. Typed is OK.
1st period seniors: Question 5
2nd period seniors: Question 4
6th and 7th period seniors: Question 1
The random assignment of questions for sophomores and juniors will take place on Tuesday.
DO NOT TALK ABOUT MULTIPLE CHOICE EXAM QUESTIONS. We can talk about the free response questions starting Friday. This means that you cannot write, text, or twitter about the questions, either.
Good luck on the test Tuesday! Please bring pencils, pens, calculator, tissues, and ID.
DO NOT BRING any books, notes, food, drinks, noisy things, cell phones, cameras, fireworks, explosives, plutonium-based products, live animals, fruits or vegetables, etc.
Plans for the rest of the year:
Recognizing that many of you will be taking other exams between now and the final, we will be working ASMA tests, reviewing adv algebra and trigonometry, developing rubrics for the questions you see on Tuesday, and preparing for the final.
1st - 5
2nd - 2
6th - 6
7th - 5
Answer completely and correctly. Bring it with you to the exam along with a calculator and a pencil, but no notebooks or backpacks. We need to cut down on the end-of-year littering around the school neighborhood.
Senior take-home exam assignments: Bring a perfect and complete response to the assigned question on the day of your final along with your textbook and green t-table card. Typed is OK.
1st period seniors: Question 5
2nd period seniors: Question 4
6th and 7th period seniors: Question 1
The random assignment of questions for sophomores and juniors will take place on Tuesday.
DO NOT TALK ABOUT MULTIPLE CHOICE EXAM QUESTIONS. We can talk about the free response questions starting Friday. This means that you cannot write, text, or twitter about the questions, either.
Good luck on the test Tuesday! Please bring pencils, pens, calculator, tissues, and ID.
DO NOT BRING any books, notes, food, drinks, noisy things, cell phones, cameras, fireworks, explosives, plutonium-based products, live animals, fruits or vegetables, etc.
Plans for the rest of the year:
Recognizing that many of you will be taking other exams between now and the final, we will be working ASMA tests, reviewing adv algebra and trigonometry, developing rubrics for the questions you see on Tuesday, and preparing for the final.
Wednesday, April 29, 2009
Chapter 15 and other topics
E-mail your edited chapter summary to jhl2881@students.kennesaw.edu as an attachment.
You will receive an invitation to join a private Wiki.
Do not put your name on the document, but DO put your name in the email title.
SENIORS IN 1st and 2nd PERIODS: Go to Room 808 for class on Wednesday.
Pre-testing processing of the exam forms for AP testing (otherwise known as the Bubbling-in sessions) have started. Go to the theater at 7:30 in the AM or 3:30 in the PM to fill in your forms in anticipation of the big day.
Next test: Cumulative multiple choice test on Thursday, April 16.
Test after that: TUESDAY, April 21. (Unless you sign up for Monday afternoon free response testing.)
We plan to test on Chapter 15 on Tuesday, April 14. Until then we will be doing problems from old exams that relate to linear regression and inferences about the slope (the problems you Hawaii folks picked up on Tuesday!!!). We covered this stuff first semester when we did regression.
Our tentative plans for tests for the rest of the semester. . .
4/14 Chapter 15
4/15 Sophomore testing in the morning
4/16 Multiple choice test #1
4/21 Multiple choice test #2
4/23 Multiple choice test #3
week of April 20-24 Free response test after school 3:45 - 5:15 one day
May 5 the big one!
Sometime later Final exam
HW due Thursday
Write up the responses to the three free response questions discussed in class in your spiral notebooks.
Notes for the 2008 problem, part c: Follow their directions. Average the two proportions. For the standard deviation you will have to find the square root of the variance of the average. Yiles! Sounds difficult.
Variance of the average = 1/4 variance of x + 1/4 variance of y.
You will receive an invitation to join a private Wiki.
Do not put your name on the document, but DO put your name in the email title.
SENIORS IN 1st and 2nd PERIODS: Go to Room 808 for class on Wednesday.
Pre-testing processing of the exam forms for AP testing (otherwise known as the Bubbling-in sessions) have started. Go to the theater at 7:30 in the AM or 3:30 in the PM to fill in your forms in anticipation of the big day.
Next test: Cumulative multiple choice test on Thursday, April 16.
Test after that: TUESDAY, April 21. (Unless you sign up for Monday afternoon free response testing.)
We plan to test on Chapter 15 on Tuesday, April 14. Until then we will be doing problems from old exams that relate to linear regression and inferences about the slope (the problems you Hawaii folks picked up on Tuesday!!!). We covered this stuff first semester when we did regression.
Our tentative plans for tests for the rest of the semester. . .
4/14 Chapter 15
4/15 Sophomore testing in the morning
4/16 Multiple choice test #1
4/21 Multiple choice test #2
4/23 Multiple choice test #3
week of April 20-24 Free response test after school 3:45 - 5:15 one day
May 5 the big one!
Sometime later Final exam
HW due Thursday
Write up the responses to the three free response questions discussed in class in your spiral notebooks.
Notes for the 2008 problem, part c: Follow their directions. Average the two proportions. For the standard deviation you will have to find the square root of the variance of the average. Yiles! Sounds difficult.
Variance of the average = 1/4 variance of x + 1/4 variance of y.
Friday, March 27, 2009
Chapter 14 Chi-square procedures
We have covered all the new material from this chapter. Your test will be on Tuesday, March 31.
HW for this weekend: AT LEAST three problems (not all odd) from the Chapter 14 chapter review. If you are struggling, do more problems. Bring all your CH 14 homework for credit on Tuesday.
Preview for after the test: We will be re-doing inference for regression (linear regression t-tests and confidence intervals) and power of the test.
Problems 11, 15, 16, and 24 are due Friday.
Problems 14.3, .4, .5, and .8 are due Wednesday.
HW due Tuesday: Using the data from your M&M bag, compare the sample distribution with the OLD theoretical distribution of BROWN 30%, RED 20%, YELLOW 20%, BLUE 10%, ORANGE 10%, and GREEN 10%. Perform a complete goodness of squares analysis of your data. If you misplaced your data, I guess you'll have to use a second bag of M&Ms. A complete analysis includes all the elements of SCAD.
HW for this weekend: AT LEAST three problems (not all odd) from the Chapter 14 chapter review. If you are struggling, do more problems. Bring all your CH 14 homework for credit on Tuesday.
Preview for after the test: We will be re-doing inference for regression (linear regression t-tests and confidence intervals) and power of the test.
Problems 11, 15, 16, and 24 are due Friday.
Problems 14.3, .4, .5, and .8 are due Wednesday.
HW due Tuesday: Using the data from your M&M bag, compare the sample distribution with the OLD theoretical distribution of BROWN 30%, RED 20%, YELLOW 20%, BLUE 10%, ORANGE 10%, and GREEN 10%. Perform a complete goodness of squares analysis of your data. If you misplaced your data, I guess you'll have to use a second bag of M&Ms. A complete analysis includes all the elements of SCAD.
Wednesday, March 18, 2009
Chapter 13 Two-sample tests
We're starting with tests of differences between two proportions. Usually our hypothesis is that there is no difference. Of course, we could look for a difference! Testing on Thursday, 3/19.
Bring all your HW from this chapter to the test on Thursday.
Problems 46 and 48 are due Wednesday.
Problems 13.41-44 are due Tuesday. Also, review your rules for variances. The variance of the difference of two means is equal to the sum of the variances of the two means. What is the variance of x-bar minus 3*y-bar if x and y are independent? Know your stuff.
Problems 15-18 should be done for Monday. Also, complete the hypothesis test from class:
Ho: mu E - mu N = 0 vs Ha: mu E -mu N < mu =" 7.26" dev =" 6.94" n =" 100" mu =" 9.55" dev =" 5.88" n =" 100" color="#ff0000">Your test on this chapter is on Thursday of next week.
HW due Thursday: Problems from the book 13.2, 3, 5, and 27, PLUS complete SCAD write-ups of the hypothesis test and confidence intervals for the differences in proportions from the census data linked below. We are looking for the difference between the % of adult Americans who have graduated from high school for women and for men.
Interesting 2-proportion statistic: http://www.census.gov/Press-Release/www/releases/archives/education/000818.html
People in the Lassiter area are happier than most: http://www.ajc.com/health/content/health/stories/2009/03/11/states_of_happiness_georgia.html?cxntlid=homepage_tab_newstab
HW due Wednesday: write up a complete (SCAD) response to the activity in class today. PLUS, read and create an outline for the second section of chapter 13.
Bring all your HW from this chapter to the test on Thursday.
Problems 46 and 48 are due Wednesday.
Problems 13.41-44 are due Tuesday. Also, review your rules for variances. The variance of the difference of two means is equal to the sum of the variances of the two means. What is the variance of x-bar minus 3*y-bar if x and y are independent? Know your stuff.
Problems 15-18 should be done for Monday. Also, complete the hypothesis test from class:
Ho: mu E - mu N = 0 vs Ha: mu E -mu N < mu =" 7.26" dev =" 6.94" n =" 100" mu =" 9.55" dev =" 5.88" n =" 100" color="#ff0000">Your test on this chapter is on Thursday of next week.
HW due Thursday: Problems from the book 13.2, 3, 5, and 27, PLUS complete SCAD write-ups of the hypothesis test and confidence intervals for the differences in proportions from the census data linked below. We are looking for the difference between the % of adult Americans who have graduated from high school for women and for men.
Interesting 2-proportion statistic: http://www.census.gov/Press-Release/www/releases/archives/education/000818.html
People in the Lassiter area are happier than most: http://www.ajc.com/health/content/health/stories/2009/03/11/states_of_happiness_georgia.html?cxntlid=homepage_tab_newstab
HW due Wednesday: write up a complete (SCAD) response to the activity in class today. PLUS, read and create an outline for the second section of chapter 13.
Wednesday, March 04, 2009
Chapter 12 Tests about means and proportions
If you missed the test on Monday, please make it up Tuesday in room 214 at 7:20 AM. If you are involved in Model UN, please make it up in room 313 at 7:20 on Wednesday morning.
In this VERY SHORT chapter we practiced the methods that we use for simple tests in the real world.
Test is Monday!!! Please try out the online interactive software Crunch It that the publisher provides. Just search on Crunch It. It does a lot of the same things that Minitab does and in the same ways.
HW due Friday: Because the problems from last night were mostly odds, tonight's assignment involves evens. Do two even problems from the chapter review. Your test is Monday.
HW due Thursday: EITHER 12.9, 19, & 37 OR 12.3, 13, 23, 29, 31, & 34.
To get credit, all work must be shown. Copying out of the back of the book will not suffice.
HW due Wednesday: 12.15, .16, .18,. .24, & .26.
HW due Monday: Read through the first section, taking notes on the key differences between previous chapters and this one. Pay particular attention to the standard errors and the kind of test used as well as the changes to assumptions/conditions. Work problems 12.2, 12.4, 12.5, 12.6, and 12.12.
In this VERY SHORT chapter we practiced the methods that we use for simple tests in the real world.
Test is Monday!!! Please try out the online interactive software Crunch It that the publisher provides. Just search on Crunch It. It does a lot of the same things that Minitab does and in the same ways.
HW due Friday: Because the problems from last night were mostly odds, tonight's assignment involves evens. Do two even problems from the chapter review. Your test is Monday.
HW due Thursday: EITHER 12.9, 19, & 37 OR 12.3, 13, 23, 29, 31, & 34.
To get credit, all work must be shown. Copying out of the back of the book will not suffice.
HW due Wednesday: 12.15, .16, .18,. .24, & .26.
HW due Monday: Read through the first section, taking notes on the key differences between previous chapters and this one. Pay particular attention to the standard errors and the kind of test used as well as the changes to assumptions/conditions. Work problems 12.2, 12.4, 12.5, 12.6, and 12.12.
Monday, February 23, 2009
Chapter 11 Tests for significance
SIGN UP FOR AP EXAMS!
Check THIS website for an article about some of our superstars of statistics.
The applet on this webpage should be enlightening regarding Type I and Type II error. Scroll down the linked page a bunch until you find the yellow box entitled Statistical Errors Applet. Read the information in the little yellow box and click on the link where it says Applet 1. Statistical Errors near the little graph to display the applet. Move the box in the scroll bar at the top to change the value of alpha (the probability of a Type I error). In real life you can change this value, but pick your alpha before you collect your data! Otherwise, you might be accused of manipulating the data and giving statisticiansa bad name.
Now, move the middle of a NEW and IMPROVED distribution by sliding the box in the scroll bar at the bottom of the window. See what the yellow region looks like when you overlap the distributions. The yellow area represents the probability of a Type II error.
So, what effect does changing alpha have on the probabilty of a Type II error? When is beta maximized? When is it minimized?
TYPE I and TYPE II errors
PLEASE read the section in the book regarding these topics.
You will only be able to calculate a POWER or a BETA (the probability of a Type II error) when some NEW mean is introduced. The power of the test is the probability that the test will be able to distinguish between your original hypothesized mu and the newly proposed mu. The probability of an error is BETA.
To calculate BETA:
Find the boundaries of the FTR region for your original hypothesis. Find the probability that x-bar would fall between that lower bound and upper bound GIVEN the NEW mu and standard error of the mean. In calculator language [that you would NEVER write on a test] it would be normcdf(LB, UB, NEWmu, sigma of x-bar).
HW due Wednesday: 11.36-11.40. Your test is Thursday.
You should have worked problems 11.5, .6, .27, .28, .29, .30, .49, .50, & .51 by Tuesday. Your test is Thursday.
The excerpt in class today was from The Lady Tasting Tea by David Salsburg.
HW due Thursday: 11.3, 11.4, 11.6
Please note that (1) null hypotheses ALWAYS have an "equals" concept
(2) null and alternative hypotheses do NOT include statistics.
In inference testing, the results of our sample may make us reject the null hypothesis if they are so unlikely that they would be unbelievably unlikely due to randomness.
Please read through the top of page 693 AND register for the AP exam.
Check THIS website for an article about some of our superstars of statistics.
The applet on this webpage should be enlightening regarding Type I and Type II error. Scroll down the linked page a bunch until you find the yellow box entitled Statistical Errors Applet. Read the information in the little yellow box and click on the link where it says Applet 1. Statistical Errors near the little graph to display the applet. Move the box in the scroll bar at the top to change the value of alpha (the probability of a Type I error). In real life you can change this value, but pick your alpha before you collect your data! Otherwise, you might be accused of manipulating the data and giving statisticiansa bad name.
Now, move the middle of a NEW and IMPROVED distribution by sliding the box in the scroll bar at the bottom of the window. See what the yellow region looks like when you overlap the distributions. The yellow area represents the probability of a Type II error.
So, what effect does changing alpha have on the probabilty of a Type II error? When is beta maximized? When is it minimized?
TYPE I and TYPE II errors
PLEASE read the section in the book regarding these topics.
You will only be able to calculate a POWER or a BETA (the probability of a Type II error) when some NEW mean is introduced. The power of the test is the probability that the test will be able to distinguish between your original hypothesized mu and the newly proposed mu. The probability of an error is BETA.
To calculate BETA:
Find the boundaries of the FTR region for your original hypothesis. Find the probability that x-bar would fall between that lower bound and upper bound GIVEN the NEW mu and standard error of the mean. In calculator language [that you would NEVER write on a test] it would be normcdf(LB, UB, NEWmu, sigma of x-bar).
HW due Wednesday: 11.36-11.40. Your test is Thursday.
You should have worked problems 11.5, .6, .27, .28, .29, .30, .49, .50, & .51 by Tuesday. Your test is Thursday.
The excerpt in class today was from The Lady Tasting Tea by David Salsburg.
HW due Thursday: 11.3, 11.4, 11.6
Please note that (1) null hypotheses ALWAYS have an "equals" concept
(2) null and alternative hypotheses do NOT include statistics.
In inference testing, the results of our sample may make us reject the null hypothesis if they are so unlikely that they would be unbelievably unlikely due to randomness.
Please read through the top of page 693 AND register for the AP exam.
Wednesday, February 04, 2009
Chapter 10 Confidence Intervals
Your test on Chapter 10 will be Tuesday, February 17.
HW due Friday: Either problem 10.53 worked out in detail showing all work or problems 10.54 and 10.58 worked cout completely.
Have you hugged your study guide lately????
HW due Thursday: Problems 10.38 and .44. 1st and 2nd periods, please bring all HW from this week on Thursday.
Today we computed paired t confidence intervals for the difference in grip strength between right and left hands.
You can find the t* value for any number of df by using the calculator;
STAT TESTS T-INT Stats x-bar = 0, sx = sqrt df+1, n = df+1, conf level = whatever you need, like .95.
ALL students should have finished 10.28, 10.30, 10.31, and 10.31 PLUS the summary of the cautions. Have these with you on Wednesday.
HW for 1st and 2nd periods: Summarize the cautions of section 10.1 (pages 635-637) in your own words and work problems 10.28 and 10.30.
Periods 6 & 7: Work problems 10.7-10.10 PLUS summarize the cautions above.
The question was raised: Why do we use 2 sometimes and 1.96 other times for Z*? As you probably recall, approximately 95% of the data in a Normal distribution will fall within about 2 standard deviations of the mean, but that was just an estimate. The more precise number of standard deviations that form the 95% boundaries is 1.96. Use that whenever we are using Z procedures UNLESS we are just looking for a quick and dirty estimate. but NOT when we are constructing confidence intervals.
When do we use sx and when do we use sigmax? Sigma represents the population standard deviation, a number we rarely know. On the other hand, sx represents our sample standard deviation. When we do not know the population standard deviation we will use t procedures instead of z procedures.
And, of course, we divide by sqrt of n to convert these standard deviations into standard errors of x-bar.
Some web-based applets for Confidence Intervals: Rice Univ Freeman
HW due Friday--
1st and 2nd per: Problems 10.7-10.10 from the text. You should have already worked the problems from the REVIEW III on pages 610 and 611.
6th and 7th per: "Review III" questions following Chapter 9 on pages 610-611 in the text AND print one page from a confidence interval applet from the web and be able to explain it.
Key concepts from today: Approximately 95% of sample averages will fall within about 2 std dev/Sqrt(n) of the population mean. If we don't know what the population mean is, we might reason that our point estimate (x-bar) is a pretty good guess, and that 95% of the time, our sample averages will fall within 2 std dev/sqrt(n) of the true mean. Then the interval (x-bar minus 2*std dev/sqrt(n), x-bar plus 2*std dev/sqrt(n)) is our confidence interval or reasonable guess at the value of the population mean. About 95% of these intervals will capture the true mean. The distance from the mean to the upper bound (or event the lower bound) is the margin of error.
These are NOT true: 95% of the time this interval contains the mean. 95% of population means fall inside this interval. 95% of the time the mean falls between lower bound and upper bound. NONE of these are true, so DO NOT write these as interpretations of the confidence intervals.
Instead, we are 95% confident that the mean falls between the lower bound and the upper bound.
If you did not work problems from the review following Chapter 9, now is the time!!!!
HW due Friday: Either problem 10.53 worked out in detail showing all work or problems 10.54 and 10.58 worked cout completely.
Have you hugged your study guide lately????
HW due Thursday: Problems 10.38 and .44. 1st and 2nd periods, please bring all HW from this week on Thursday.
Today we computed paired t confidence intervals for the difference in grip strength between right and left hands.
You can find the t* value for any number of df by using the calculator;
STAT TESTS T-INT Stats x-bar = 0, sx = sqrt df+1, n = df+1, conf level = whatever you need, like .95.
ALL students should have finished 10.28, 10.30, 10.31, and 10.31 PLUS the summary of the cautions. Have these with you on Wednesday.
HW for 1st and 2nd periods: Summarize the cautions of section 10.1 (pages 635-637) in your own words and work problems 10.28 and 10.30.
Periods 6 & 7: Work problems 10.7-10.10 PLUS summarize the cautions above.
The question was raised: Why do we use 2 sometimes and 1.96 other times for Z*? As you probably recall, approximately 95% of the data in a Normal distribution will fall within about 2 standard deviations of the mean, but that was just an estimate. The more precise number of standard deviations that form the 95% boundaries is 1.96. Use that whenever we are using Z procedures UNLESS we are just looking for a quick and dirty estimate. but NOT when we are constructing confidence intervals.
When do we use sx and when do we use sigmax? Sigma represents the population standard deviation, a number we rarely know. On the other hand, sx represents our sample standard deviation. When we do not know the population standard deviation we will use t procedures instead of z procedures.
And, of course, we divide by sqrt of n to convert these standard deviations into standard errors of x-bar.
Some web-based applets for Confidence Intervals: Rice Univ Freeman
HW due Friday--
1st and 2nd per: Problems 10.7-10.10 from the text. You should have already worked the problems from the REVIEW III on pages 610 and 611.
6th and 7th per: "Review III" questions following Chapter 9 on pages 610-611 in the text AND print one page from a confidence interval applet from the web and be able to explain it.
Key concepts from today: Approximately 95% of sample averages will fall within about 2 std dev/Sqrt(n) of the population mean. If we don't know what the population mean is, we might reason that our point estimate (x-bar) is a pretty good guess, and that 95% of the time, our sample averages will fall within 2 std dev/sqrt(n) of the true mean. Then the interval (x-bar minus 2*std dev/sqrt(n), x-bar plus 2*std dev/sqrt(n)) is our confidence interval or reasonable guess at the value of the population mean. About 95% of these intervals will capture the true mean. The distance from the mean to the upper bound (or event the lower bound) is the margin of error.
These are NOT true: 95% of the time this interval contains the mean. 95% of population means fall inside this interval. 95% of the time the mean falls between lower bound and upper bound. NONE of these are true, so DO NOT write these as interpretations of the confidence intervals.
Instead, we are 95% confident that the mean falls between the lower bound and the upper bound.
If you did not work problems from the review following Chapter 9, now is the time!!!!
Friday, January 30, 2009
Chapter 9 Sampling Distributions
If you missed the test on Tuesday, take it Tuesday PM at 3:30 in Mrs. Prestwood's classroom. HW for tonight: Do at least 5 of the 10 problems in REVIEW 3 which follows Chapter 9. Get ready for confidence intervals!!!!
http://www.stat.sc.edu/~west/javahtml/ConfidenceInterval.html
Prepare for the test by working problems from the text and by using a study guide (if you have one) to practice with multiple choice problems. You are welcome to come by in the morning to use a study guide in the classroom.
Your test on Chapter 9 is Tuesday, snow or no snow. Work lots of problems from the chapter. Be sure that you know how to check assumptions or conditions. Do you know when you are calculating probabilities for means and when you are calculating probabilities for proportions? You have to use the right conditions and formulas or you won't be answering the question.
Oh yeah, CiCi's Sunday. Super Bowl Sunday.
For Thursday, 1st and 2nd periods: Complete the questions from the AP exams that we looked at in class. The first one asked for (1) the probability that a measurement of a depth of 2 was negative when the error of the measurement was Normally distributed with mean 0 and std dev 1.5.
(2) What is the probability that at least one of three independent measurements from this distribution was negative?
(3) What is the probability that the average of three independent measurements from this distribution was negative?
Everybody needs to work problem 3 from the 2007 exam.
HW Problems 9.20, .21, 25., .26, &.29 due Wednesday.
HW Problems 9.19, 9.27, 9.30 due Tuesday.
Summary of the three sections of the chapter:
A sampling distribution is the distribution of the sample means of all possible samples of size n. As n (the sample size) increases, the variability of the sample means decreases.
When the underlying (original) distribution is Normally distributed, the sampling distribution for samples of any size n will be Normally distributed.
When the underlying (original) distribution is NOT Normally distributed, the sampling distribution for large sample sizes will be approximately Normally distributed. The closer the original distribution was to Normal, the smaller the sample size required to make the sampling distribution approximately Normally distributed.
These concepts can be applied easily to two cases: measures of x and sample proportions.
For measures of x: The mean of the sampling distribution of x bar is the mean of the underlying distribution of x. The standard deviation of the sampling distribution of x bar is the standard deviation of the underlying distribution /the square root of n.
For sample proportions: When np and nq are both > 10 and n is less than 1/10 of the population, the mean of the p hats is p and the standard deviation of the p hats is the square root of p*q/n AND the distribution of p hats is approximately normal.
< Link to a history of the penny.
Link to a more official history of the penny.
HW Problems 9.32 and 9.34.
I will NOT be available at Open House Thursday night. Please email me with any concerns or join us at CiCi's on Sunday.
HW due Friday, 1/23: 9.10, 9.12, 9.14. Students from per 1 and 2, email your averages to Mrs. L if you did not load them in class. Periods 6 and 7, look up the phrase "planned obsolescence."
This chapter requires you to recall some vocabulary from previous chapters.
HW due Thursday, 1/22: Problems 9.1, .7a-e, .9, .11, .13. You should read through the sections in order to understand the questions.
Also, periods 1 and 2, bring five results from mean(randBin(100,.5,100)).
Measures of central tendency
Median
Mean
Mode
Measures of dispersion (spread)
Range
Standard deviation
Variance
Interquartile range
Absolute deviation
Graphical displays
histogram
line graph
stem and leaf
box and whisker graph
probability density function
scatterplot
cumulative density function
dot plot
pie graph
bar graphs
Pictures speak louder than words
μ = population mean x bar = sample mean (unbiased estimator of mean)
If a sample is drawn at random from a population, the mean of the sample is an excellent estimator of the mean of the population.
σ = population standard deviation s = sample standard deviation
Recall that the calculation of s requires division by n-1 for some complicated reasons.
sx is the standard deviation of the distribution of x
is the standard deviation of the means of the samples of x
E[x] = E[ x bar]
http://www.stat.sc.edu/~west/javahtml/ConfidenceInterval.html
Prepare for the test by working problems from the text and by using a study guide (if you have one) to practice with multiple choice problems. You are welcome to come by in the morning to use a study guide in the classroom.
Your test on Chapter 9 is Tuesday, snow or no snow. Work lots of problems from the chapter. Be sure that you know how to check assumptions or conditions. Do you know when you are calculating probabilities for means and when you are calculating probabilities for proportions? You have to use the right conditions and formulas or you won't be answering the question.
Oh yeah, CiCi's Sunday. Super Bowl Sunday.
For Thursday, 1st and 2nd periods: Complete the questions from the AP exams that we looked at in class. The first one asked for (1) the probability that a measurement of a depth of 2 was negative when the error of the measurement was Normally distributed with mean 0 and std dev 1.5.
(2) What is the probability that at least one of three independent measurements from this distribution was negative?
(3) What is the probability that the average of three independent measurements from this distribution was negative?
Everybody needs to work problem 3 from the 2007 exam.
HW Problems 9.20, .21, 25., .26, &.29 due Wednesday.
HW Problems 9.19, 9.27, 9.30 due Tuesday.
Summary of the three sections of the chapter:
A sampling distribution is the distribution of the sample means of all possible samples of size n. As n (the sample size) increases, the variability of the sample means decreases.
When the underlying (original) distribution is Normally distributed, the sampling distribution for samples of any size n will be Normally distributed.
When the underlying (original) distribution is NOT Normally distributed, the sampling distribution for large sample sizes will be approximately Normally distributed. The closer the original distribution was to Normal, the smaller the sample size required to make the sampling distribution approximately Normally distributed.
These concepts can be applied easily to two cases: measures of x and sample proportions.
For measures of x: The mean of the sampling distribution of x bar is the mean of the underlying distribution of x. The standard deviation of the sampling distribution of x bar is the standard deviation of the underlying distribution /the square root of n.
For sample proportions: When np and nq are both > 10 and n is less than 1/10 of the population, the mean of the p hats is p and the standard deviation of the p hats is the square root of p*q/n AND the distribution of p hats is approximately normal.
< Link to a history of the penny.
Link to a more official history of the penny.
HW Problems 9.32 and 9.34.
I will NOT be available at Open House Thursday night. Please email me with any concerns or join us at CiCi's on Sunday.
HW due Friday, 1/23: 9.10, 9.12, 9.14. Students from per 1 and 2, email your averages to Mrs. L if you did not load them in class. Periods 6 and 7, look up the phrase "planned obsolescence."
This chapter requires you to recall some vocabulary from previous chapters.
HW due Thursday, 1/22: Problems 9.1, .7a-e, .9, .11, .13. You should read through the sections in order to understand the questions.
Also, periods 1 and 2, bring five results from mean(randBin(100,.5,100)).
Measures of central tendency
Median
Mean
Mode
Measures of dispersion (spread)
Range
Standard deviation
Variance
Interquartile range
Absolute deviation
Graphical displays
histogram
line graph
stem and leaf
box and whisker graph
probability density function
scatterplot
cumulative density function
dot plot
pie graph
bar graphs
Pictures speak louder than words
μ = population mean x bar = sample mean (unbiased estimator of mean)
If a sample is drawn at random from a population, the mean of the sample is an excellent estimator of the mean of the population.
σ = population standard deviation s = sample standard deviation
Recall that the calculation of s requires division by n-1 for some complicated reasons.
sx is the standard deviation of the distribution of x
is the standard deviation of the means of the samples of x
E[x] = E[ x bar]
Wednesday, January 14, 2009
Chapter 8 and the new semester
HW due Thursday: Problems 8.41, 8.43, and 8.44 from the text.
HW due Wednesday: Problems 8.45-8.50. Your test is Tuesday of next week--the day after the Dr. King holiday.
How are these questions similar? How are they different? What strategies would you use to answer each?
1. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 with replacement will not accept text messaging?
2. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 WITHOUT replacement will not accept text messaging?
3. Of the 200,000 cell phones in a metropolitan community, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 WITHOUT replacement will not accept text messaging?
HW due Tuesday, January 13: Probloems 8.19-8.24.
HW due Friday: 8.7, 8.10, 8.11, 8.13, & 8.16.
By Monday, make sure that all of the assigned homework has been done correctly and completely.
HW due Thursday: Problems 1-6 of Chapter 8. Each question requires that you explain how the 4 characteristics is satisfied. Also, define x in each setting. KEY: If your are not counting the number of successes (x) in n trials, it can't possibly be a binomial. If is IS, then check the rest of the conditions.
Yippee! We made to the home stretch.
We will begin Chapter 8 on Wednesday. Tuesday's HW is to complete as much of the crossword puzzle as possible. Some of the answers will become clearer as we progress through binomial and geometric distributions. The plan is to test on Chapter 8 next week and have a chapter test every 2-3 weeks thereafter. This way, we'll be able to dedicate the time after the break to review for the exam.
Let's see. Remove Mirage. Replace batteries. Ask parents to read and sign the syllabus. Bring paper, pencil, and calculator on Wednesday. Be safe.
Did I forget anything? :)
HW due Wednesday: Problems 8.45-8.50. Your test is Tuesday of next week--the day after the Dr. King holiday.
How are these questions similar? How are they different? What strategies would you use to answer each?
1. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 with replacement will not accept text messaging?
2. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 WITHOUT replacement will not accept text messaging?
3. Of the 200,000 cell phones in a metropolitan community, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 WITHOUT replacement will not accept text messaging?
HW due Tuesday, January 13: Probloems 8.19-8.24.
HW due Friday: 8.7, 8.10, 8.11, 8.13, & 8.16.
By Monday, make sure that all of the assigned homework has been done correctly and completely.
HW due Thursday: Problems 1-6 of Chapter 8. Each question requires that you explain how the 4 characteristics is satisfied. Also, define x in each setting. KEY: If your are not counting the number of successes (x) in n trials, it can't possibly be a binomial. If is IS, then check the rest of the conditions.
Yippee! We made to the home stretch.
We will begin Chapter 8 on Wednesday. Tuesday's HW is to complete as much of the crossword puzzle as possible. Some of the answers will become clearer as we progress through binomial and geometric distributions. The plan is to test on Chapter 8 next week and have a chapter test every 2-3 weeks thereafter. This way, we'll be able to dedicate the time after the break to review for the exam.
Let's see. Remove Mirage. Replace batteries. Ask parents to read and sign the syllabus. Bring paper, pencil, and calculator on Wednesday. Be safe.
Did I forget anything? :)
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