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!
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