HW due Thursday: Problems 10.67 and 10.68 PLUS create a study guide for Chapter 10. YOUR TEST will be Tuesday, March 4. This is a short day, so you will have to think fast! HW due Monday: 10.70, 10.71, 10.78, 10.81, 10.82, 10.86. In addition to reviewing, we will be taking an ASMA test and starting Chapter 11 Thursday, Friday, and Monday.
HW due Wednesday: Problems 39, 40, and 43 done completely. Answers from the calculator are not sufficient.
HW due Tuesday, Feb 26: Problems 27, 28, 33, and 34 covering hypothesis testing. You may need to refer to the PHANTOMS side of the worksheet. If you have difficulty writing hypotheses, do problems 30, 31, and 32 as well.
RE: Hypotheses writing
The hypotheses always include PARAMETERS, not statistics. Use mu and p, not x-bar and p-hat. The null hypothesis always has an "equal to" nature rather than a greater than or less than.
HW due Monday, Feb 25: Problems from Chapter 10 (5, 12, 13, 14, 15). You will need to read the subsection, example, and info box before problem 13 to do the last few problems.
The AP registration deadline is upon us! Go to the Lassiter homepage and register for your exams. Bring a check to Ms Gasaway tomorrow.
HW for Friday, Feb 22: Do problems from Chapter 10: 10.6, 10.7, and 10.8 using your choice of SCAD or PHANTOMS and PANIC. The answers should be complete!
HW due Thursday, Feb 21: RE-DO problems 12.6-12.9 using the PHANTOMS or PANIC guides handed out in class. For those who miss Thursday's class due to a field trip, bring all homework on the day you return to demonstrate that you are current in the class or I will assign a more comprehensive set of problems upon your return to catch you up.
For Friday, Feb 22: continue to create confidence intervals, this time using x-bar and sigma of x. Do problems from Chapter 10: 10.6, 10.7, and 10.8. What assumptions or conditions do you need to check? If you guessed (1) SRS and independent observations, (2) population distribution is approximately normally distributed (or your sample is large enough for the central limit theorem to apply), and (3) the sample is less than one-tenth of the population size, then your brain is a finely-tuned instrument.
As you recall from Friday, the formula for the confidence interval for one proportion is p-hat +/- z* times SQRT(p-hat*(1-p-hat)/n)).
The source of the handout in today's class is
http://www.district196.org/evhs/People/baileyrcweb/APS%20Files/APS%20Main.htm
Please strike through the references to "retaining" the null hypothesis as well as the graph of a normal distribution on the confidence interval page. These are not appropriate for AP Statistics.
HW due Wednesday, Feb 20: 12.8 and 12.9 with complete solutions.
HW due Friday: Journal entry using problem 3 from the 2006 AP exam PLUS problems 12.6 and 12.7 from the text.
Alpha = the probability of rejecting the null hypothesis when the null hypothesis is true. It is the probability of a Type 1 error. This is the area associated with the rejection region.
HW due Thursday: Finish the 4-page worksheet about Distracted Drivers. Work on your journal entry (due Friday in a composition notebook).
HW due Tuesday: Problems 12.4 and 12.5. You'll have to read the information on the two pages preceding these questions. Come to class prepared to (1) explain how likely/unlikely your sample of pom-poms was from today's activity. That means that you have to calculate the z-value for your observation and compute the probability in the tail. ALSO, (2) be ready to explain how to simulate the distracted driver scenario using cards.
HW due Monday: Page 7 of 2006 Form B, problem 3 (golf balls) AND figure out a way to simulate the situation for problem 5 on page 9 of 2007 (the cell phone distraction problem).
JOURNAL ENTRY: The complete, perfect write-up of problem 3 from 2006 (page 8) will be due on Friday. The problem should be the first part of the entry, your fabulous answer should follow. This is the first problem to be entered in your composition notebook.
Has anyone tried this website? http://stattrek.com/AP-Statistics-1/AP-Statistics-Intro.aspx?Tutorial=ap
I wondered if it was helpful. Please let me know.
Saturday, February 23, 2008
Monday, February 04, 2008
Chapter 9 Sampling Distributions
Welcome to the beginning of inferential statistics! Your test is Thursday February 7.
Elaborate response to a question about mu and x-bar is in the comments section below. Don't miss it.
Work all the problems on the latest problem worksheet for homework Tuesday.
Mean of sampling distribution = mean of population regardless of shape of distribution
Std dev of sampling distribution = std dev of population divided by sqrt (n) regardless of shape of distribution as long as sample does not exceed 1/10th population.
Central Limit Theorem
Case 0: Underlying distribution is normal à sampling distribution is AUTOMATICALLY normal. The Central Limit Theorem DOES NOT APPLY. It isn't needed.
Case 1: If the sample is tiny (less than or equal to 10), then the population distribution must be nearly normal for the Central Limit Theorem to kick in.
Case 2: If the sample is moderate (up to about 35), then the population needs to be mound shaped without outliers for the Central Limit Theorem to kick in.
Case 3: If the sample is large, then the Central Limit Theorem kicks in.
****Write the implications of the Central Limit Theorem in your own words.
Thus, the answer to the questions at the end of problems .27 and .28 from Friday are that we DID NOT need the underlying distribution to be normal for us to use the formulas for the mean and the std dev of the sampling distribution (mu x = mu x-bar and std dev x-bar = std dev x / sqrt n, as shown in the text). Knowing that the distribution of x is Normal or knowing that the CLT applies is essential to working the sampling distribution problems using Normal methods.
HW: Problems 17 through 19 on the w/s from last week AND problems 8.34-8.36 on the w/s we handed out in class today.
Here's an applet that will help to show what happens to the distribution of the sample means as the sample size increases and as the distribution of the population is more or less normal. Set the radio buttons to show only the sample means and sample 100 at a time.
http://wise.cgu.edu/sdmmod/sdm_applet.asp
As you saw in the histograms today, the larger the sample size, the narrower the distribution of sample means. In fact, the standard deviation of the distribution of sample means shrinks proportionally to 1/( square root of the sample size)[the std dev of the sampling means = sigma of x times 1/sqrt n]. You'll see this in your READING of section 9.3 and practice it in your HOMEWORK for the weekend: 9.26 through 9.29.
For those who need to refresh their understanding of histograms, do problems 1.4 and 1.41 by hand.
Don't forget about CiCi's on Sunday if you are available.
What is the probability. . . ?http://www.time.com/time/health/article/0,8599,1707541,00.html?cnn=yes
Due Friday: Work problems 12-16 on the handout. Be an expert on these proportion problems and normal approximation for the binomial before you come to class. Friday we start sampling distributions for sample means.
Due Thursday: Problems 8-11 on the handout.
Due Wednesday: Problems 9.17 and 9.18, worked and explained completely, OR problems 9.19 and 9.20, which are more routine but must be completed.
What happens when the sample size increases??? If your variable of interest is the sample proportion, the distribution of sample proportions (p-hats) will become "tighter," that is that it will have less variability as the sample size increases.
Now, if you're talking about the values of X in a binomial distribution, as the number of trials increases, the variability of the number of successes also increases. Arrrrrggggh! Sometimes the standard deviation increases, sometimes it decreases.
One of the important ideas that you were supposed to catch was that the population size does not affect the variability of the sampling distribution. You "see" this when you look at the formulas--there is no mention of the population size in the formula for the standard deviation.
So, what is the point? For those binomial distributions where the expected number of successes and the expected number of failures are both at least ten, the sampling distribution of the Xs or the p-hats may be modeled (approximately) by the normal curve. Thus, you can calculate z-values for the values of interest, X or p-hat, and use the standard normal table or normalcdf to calculate probabilities. Cool.
This is part of the foundation for the polling estimates that you see so often during these election years.
Here's a new section for the blog called Because You Asked. One of the gurus of AP Statistics wrote an article that explains the 10% rule. You can find it through College Board at the following link.
http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/39161.html
Due Tuesday: Problems 9.14 and 9.15 PLUS you must read the pages between these problems. Get your journal ready for the first entry.
Due Monday: All of the work previously assigned and a complete, correct draft of the answers to the "depth of the refracting layer" problem we worked in class on Thursday and Friday.
HW due Friday: Read through page 467 CAREFULLY. Work problems 9.1-9.4, 9.6, 9.8, 9.9, and 9.12. Do problem 9.7 if you get the chance (otherwise, it will be due later).
Parameters are measures of populations.
Statistics are measures of samples.
Examples of parameters: the mean of a population (mu, AKA mu sub x), the population proportion (p), the population standard deviation (sigma).
Examples of statistics: the sample mean (x-bar), the sample proportion (p-hat), and the sample standard deviation (s sub x).
The mean of all the sample means of a distribution (the sampling distribution) is the same as the mean of the distribution. This means that mu sub x-bar equals mu sub x.
The variability of the sample means (the variance of the sampling distribution)decreases as the sample size increases.
As long as the population is REALLY large compared to the sample, the size of the population does not affect the variability of the sample means.
HW for Thursday: Complete the blue sheet AND do problems 9.1-9.4 and 9.8.
Questions to ponder: What does the histogram of your penny-ages look like?
Does the histogram from a small sample have the same shape as a large sample's histogram?
What do you think that the average age of the pennies is?
How far out are outliers?
What are the important characteristics that you need to include when describing a probability histogram (either frequency diagram or relative frequency diagram)?
Elaborate response to a question about mu and x-bar is in the comments section below. Don't miss it.
Work all the problems on the latest problem worksheet for homework Tuesday.
Mean of sampling distribution = mean of population regardless of shape of distribution
Std dev of sampling distribution = std dev of population divided by sqrt (n) regardless of shape of distribution as long as sample does not exceed 1/10th population.
Central Limit Theorem
Case 0: Underlying distribution is normal à sampling distribution is AUTOMATICALLY normal. The Central Limit Theorem DOES NOT APPLY. It isn't needed.
Case 1: If the sample is tiny (less than or equal to 10), then the population distribution must be nearly normal for the Central Limit Theorem to kick in.
Case 2: If the sample is moderate (up to about 35), then the population needs to be mound shaped without outliers for the Central Limit Theorem to kick in.
Case 3: If the sample is large, then the Central Limit Theorem kicks in.
****Write the implications of the Central Limit Theorem in your own words.
Thus, the answer to the questions at the end of problems .27 and .28 from Friday are that we DID NOT need the underlying distribution to be normal for us to use the formulas for the mean and the std dev of the sampling distribution (mu x = mu x-bar and std dev x-bar = std dev x / sqrt n, as shown in the text). Knowing that the distribution of x is Normal or knowing that the CLT applies is essential to working the sampling distribution problems using Normal methods.
HW: Problems 17 through 19 on the w/s from last week AND problems 8.34-8.36 on the w/s we handed out in class today.
Here's an applet that will help to show what happens to the distribution of the sample means as the sample size increases and as the distribution of the population is more or less normal. Set the radio buttons to show only the sample means and sample 100 at a time.
http://wise.cgu.edu/sdmmod/sdm_applet.asp
As you saw in the histograms today, the larger the sample size, the narrower the distribution of sample means. In fact, the standard deviation of the distribution of sample means shrinks proportionally to 1/( square root of the sample size)[the std dev of the sampling means = sigma of x times 1/sqrt n]. You'll see this in your READING of section 9.3 and practice it in your HOMEWORK for the weekend: 9.26 through 9.29.
For those who need to refresh their understanding of histograms, do problems 1.4 and 1.41 by hand.
Don't forget about CiCi's on Sunday if you are available.
What is the probability. . . ?http://www.time.com/time/health/article/0,8599,1707541,00.html?cnn=yes
Due Friday: Work problems 12-16 on the handout. Be an expert on these proportion problems and normal approximation for the binomial before you come to class. Friday we start sampling distributions for sample means.
Due Thursday: Problems 8-11 on the handout.
Due Wednesday: Problems 9.17 and 9.18, worked and explained completely, OR problems 9.19 and 9.20, which are more routine but must be completed.
What happens when the sample size increases??? If your variable of interest is the sample proportion, the distribution of sample proportions (p-hats) will become "tighter," that is that it will have less variability as the sample size increases.
Now, if you're talking about the values of X in a binomial distribution, as the number of trials increases, the variability of the number of successes also increases. Arrrrrggggh! Sometimes the standard deviation increases, sometimes it decreases.
One of the important ideas that you were supposed to catch was that the population size does not affect the variability of the sampling distribution. You "see" this when you look at the formulas--there is no mention of the population size in the formula for the standard deviation.
So, what is the point? For those binomial distributions where the expected number of successes and the expected number of failures are both at least ten, the sampling distribution of the Xs or the p-hats may be modeled (approximately) by the normal curve. Thus, you can calculate z-values for the values of interest, X or p-hat, and use the standard normal table or normalcdf to calculate probabilities. Cool.
This is part of the foundation for the polling estimates that you see so often during these election years.
Here's a new section for the blog called Because You Asked. One of the gurus of AP Statistics wrote an article that explains the 10% rule. You can find it through College Board at the following link.
http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/39161.html
Due Tuesday: Problems 9.14 and 9.15 PLUS you must read the pages between these problems. Get your journal ready for the first entry.
Due Monday: All of the work previously assigned and a complete, correct draft of the answers to the "depth of the refracting layer" problem we worked in class on Thursday and Friday.
HW due Friday: Read through page 467 CAREFULLY. Work problems 9.1-9.4, 9.6, 9.8, 9.9, and 9.12. Do problem 9.7 if you get the chance (otherwise, it will be due later).
Parameters are measures of populations.
Statistics are measures of samples.
Examples of parameters: the mean of a population (mu, AKA mu sub x), the population proportion (p), the population standard deviation (sigma).
Examples of statistics: the sample mean (x-bar), the sample proportion (p-hat), and the sample standard deviation (s sub x).
The mean of all the sample means of a distribution (the sampling distribution) is the same as the mean of the distribution. This means that mu sub x-bar equals mu sub x.
The variability of the sample means (the variance of the sampling distribution)decreases as the sample size increases.
As long as the population is REALLY large compared to the sample, the size of the population does not affect the variability of the sample means.
HW for Thursday: Complete the blue sheet AND do problems 9.1-9.4 and 9.8.
Questions to ponder: What does the histogram of your penny-ages look like?
Does the histogram from a small sample have the same shape as a large sample's histogram?
What do you think that the average age of the pennies is?
How far out are outliers?
What are the important characteristics that you need to include when describing a probability histogram (either frequency diagram or relative frequency diagram)?
Wednesday, January 16, 2008
Chapter 8 Some special probability distributions
TEST Tuesday 1/22/08
HW due 1/18: 8.41, 8.42
HW due 1/17: 8.37, 8.38, 8.39
HW due 1/16: 8.27, 8.28, 8.30, 8.31
HW due 1/15: 8.24, 8.25
With apologies to our Harvard buddies, here is a summary of binomial distribution facts and methods:
http://www.stat.yale.edu/Courses/1997-98/101/binom.htm
HW due 1/14: 8.19, .20, .22, .23
You guys rocked today! Your questions and explanations were top notch. HW 1/10 Answer problem #11 fromt he worksheet in the blue book using all three of the methods: formula, binomial pdf, and binomial cdf. Show all work and include explanations that you can rely upon to remind you of these methods later in the semester. Be neat and write legibly. Use appropriate language.
HW 1/9 Answer the questions from the 12 days worksheet that have a binomial setting.
HW 1/8 Write up a study guide for the Binomial Probability section of Chapter 8 AND answer questions 8.1-8.4. Bring the "12 days" worksheet back so we can discuss it.
Check out the arbitrary (not random) stuff in the next blog!
HW due 1/18: 8.41, 8.42
HW due 1/17: 8.37, 8.38, 8.39
HW due 1/16: 8.27, 8.28, 8.30, 8.31
HW due 1/15: 8.24, 8.25
With apologies to our Harvard buddies, here is a summary of binomial distribution facts and methods:
http://www.stat.yale.edu/Courses/1997-98/101/binom.htm
HW due 1/14: 8.19, .20, .22, .23
You guys rocked today! Your questions and explanations were top notch. HW 1/10 Answer problem #11 fromt he worksheet in the blue book using all three of the methods: formula, binomial pdf, and binomial cdf. Show all work and include explanations that you can rely upon to remind you of these methods later in the semester. Be neat and write legibly. Use appropriate language.
HW 1/9 Answer the questions from the 12 days worksheet that have a binomial setting.
HW 1/8 Write up a study guide for the Binomial Probability section of Chapter 8 AND answer questions 8.1-8.4. Bring the "12 days" worksheet back so we can discuss it.
Check out the arbitrary (not random) stuff in the next blog!
Sunday, January 06, 2008
First semester final exam and other neat stuff to read
A timely article about polling: http://www.cnn.com/2008/POLITICS/01/02/projection.explainer/index.html?iref=newssearch
Article on the effect of improved organizational skills on boys' achievement in school:
http://www.iht.com/articles/2008/01/01/america/01boys.php
Have you seen the Norwegian engineering recruitment videos yet? Scroll down and let me know what you think.
For info on influential points and outliers, google statistics influential points. Some students posted pretty good (but terribly distracting) powerpoints.
The SAT results for Georgia broken down in all kinds of interesting ways:
http://www.collegeboard.com/prod_downloads/about/news_info/cbsenior/yr2007/GA_07.pdf
These data prompt discussion about causation, such as whether choosing a technical major makes your math score higher. What do you think?
On the lack of publicity for Nobel Prize Winners:
http://pharmtech.findpharma.com/pharmtech/From+the+Editor/What-Good-is-Winning-a-Prize-if-No-One-Cares/ArticleStandard/Article/detail/469658
So you want to be a casino mogul? How about starting with one of these jobs?
http://www.state.nj.us/oag/ge/2000news/slotlab.htm
Shortages of engineers (Click on the READ online button, then click on the lower right corner of the pages to advance through the newsletter)
http://thefloridaengineer.eng.ufl.edu/themagazine/fe0801/index.php
Two videos from Norway:
There's one bad word in this one written in the subtitles. Please excuse this word--the rest of the video promotes engineering for young people. (And you know how those crazy Norwegians are.)
http://www.youtube.com/watch?v=gXZZknJWtGg&feature=related
http://www.youtube.com/watch?v=JFoMmJAAHjg&feature=related
Water use statistics for Cobb: http://www.ajc.com/metro/content/metro/cobb/stories/2007/12/19/cobb_water_1220.html
Interesting webpage about one of our community members and how his company provides service in disaster relief:
http://cateringcajun.net/_wsn/page7.html
Chance, conditional probability, and MARS!
http://www.cnn.com/2007/TECH/space/12/21/mars.asteroid.ap/index.html
Article on the effect of improved organizational skills on boys' achievement in school:
http://www.iht.com/articles/2008/01/01/america/01boys.php
Have you seen the Norwegian engineering recruitment videos yet? Scroll down and let me know what you think.
For info on influential points and outliers, google statistics influential points. Some students posted pretty good (but terribly distracting) powerpoints.
The SAT results for Georgia broken down in all kinds of interesting ways:
http://www.collegeboard.com/prod_downloads/about/news_info/cbsenior/yr2007/GA_07.pdf
These data prompt discussion about causation, such as whether choosing a technical major makes your math score higher. What do you think?
On the lack of publicity for Nobel Prize Winners:
http://pharmtech.findpharma.com/pharmtech/From+the+Editor/What-Good-is-Winning-a-Prize-if-No-One-Cares/ArticleStandard/Article/detail/469658
So you want to be a casino mogul? How about starting with one of these jobs?
http://www.state.nj.us/oag/ge/2000news/slotlab.htm
Shortages of engineers (Click on the READ online button, then click on the lower right corner of the pages to advance through the newsletter)
http://thefloridaengineer.eng.ufl.edu/themagazine/fe0801/index.php
Two videos from Norway:
There's one bad word in this one written in the subtitles. Please excuse this word--the rest of the video promotes engineering for young people. (And you know how those crazy Norwegians are.)
http://www.youtube.com/watch?v=gXZZknJWtGg&feature=related
http://www.youtube.com/watch?v=JFoMmJAAHjg&feature=related
Water use statistics for Cobb: http://www.ajc.com/metro/content/metro/cobb/stories/2007/12/19/cobb_water_1220.html
Interesting webpage about one of our community members and how his company provides service in disaster relief:
http://cateringcajun.net/_wsn/page7.html
Chance, conditional probability, and MARS!
http://www.cnn.com/2007/TECH/space/12/21/mars.asteroid.ap/index.html
Tuesday, December 11, 2007
Chapter 7 Random Variables
INTERESTING NEWS:
http://news.yahoo.com/s/ap/20071213/ap_on_re_us/hiv_lawsuit
This test will be on Thursday, December 13, 2007.
You will need to create a chart to remind yourself about the formulas for this chapter until you have practiced enough to know them by heart. A sticky-note at pages 396 and 400 would also be helpful!
Mu = the POPULATION average. This is a parameter.
Sigma squared = the POPULATION variance. This is also a parameter.
Standard deviation is the square root of the variance.
X-bar is the sample average, the unbiased estimator of the population average. It is a statistic.
S-squared is the sample variance, the unbiased estimator of the population variance. It is also a statistic.
HW due Wednesday, December 12th: 7.13, 7.15, 7.17, 7.34, 7.42
HW due Tuesday, December 11th: 7.24, 7.28. Use the formulas and the examples in the text.
HW due Monday, December 10th : 7.2, 7.4, 7.7.
http://news.yahoo.com/s/ap/20071213/ap_on_re_us/hiv_lawsuit
This test will be on Thursday, December 13, 2007.
You will need to create a chart to remind yourself about the formulas for this chapter until you have practiced enough to know them by heart. A sticky-note at pages 396 and 400 would also be helpful!
Mu = the POPULATION average. This is a parameter.
Sigma squared = the POPULATION variance. This is also a parameter.
Standard deviation is the square root of the variance.
X-bar is the sample average, the unbiased estimator of the population average. It is a statistic.
S-squared is the sample variance, the unbiased estimator of the population variance. It is also a statistic.
HW due Wednesday, December 12th: 7.13, 7.15, 7.17, 7.34, 7.42
HW due Tuesday, December 11th: 7.24, 7.28. Use the formulas and the examples in the text.
HW due Monday, December 10th : 7.2, 7.4, 7.7.
Monday, December 03, 2007
Chapter 6 Probability
The Chapter 6 test will be December 6th.
Previous tests will be returned to students as soon as they are graded.
Prepare for the test. Work problems from each section. Read the chapter and section summaries. Write down what you are doing. Draw the Venn diagram or the tree diagram for complicated situations. Ask questions on the blog. Take the practice test.
Here are some answers to even HW problems:
Problem 6.10 (a) S= {all numbers between 0 and 24}
(b) = {any whole number up to and including 11,000}
(c) S = {0, 1, . . . 12}
(d) S= {any dollar and cents amount up to [insert your maximum guess here]}
(e) S = {any positive or negative number}
Problem 6.12 Four outcomes for two coins: {HH, HT, TH, TT}, eight for three coins: {HHH. HHT, HTH, HTT, THH, THT, TTH, TTT}, and sixteen for four coins (do that one yourself!).
Problem 6.16 (a) YYY -0000 through YYY-9999 = 10,000 numbers. (b) YYY-ZXX-XXXX, each X having 10 possible numbers, except the number can't start with a 0 or a 1 meaning that Z has only 8 possible values, so this means 8 * 10^6 LESS the restricted numbers (911-xxxx, 411-xxxx, etc.)
Problem 6.20 P(moves to another class) = 1 - P(stays) = 1 - .46 = .54.
Problem 6.24 P(wins large battle) = .6, P(wins three small battles) = P(wins individual small battle)^3 = .8^3 = .512. Choose the strategy with the larger probability of occurring.
Problem 6.40
Venn diagram has two circles representing getting job A and getting job B.
Both jobs: intersection of the two circles, the overlapped part, the biscuit.
First but not second: the part of circle A that is not within circle B
Second but not first: the part of circle B that is not within circle A
Neither: the part that is in the background, in NEITHER circle.
Problem 6.44
P(W) = 856/1626
P(W given prof degree) = 30/74
These are not the same. so gender and professional degree are not independent
Problem 6.56
P(y <> x) = 1/8,
P(y > x) = 1/2,
P(y <> x) = P(y <> x) /P(y > x) = 1/4.
Problem 6.48: P(W) * P(Manager given W) = P(Woman AND Manager)
One pattern that shows up a lot is Marginal * Conditional = Joint
If you divide both sides by Marginal you get
Conditional = Joint / Marginal.
IFF means IF AND ONLY IF.
IFF P(A) * P(B) = P(both A&B), A and B are independent.
Just "going through the motions" does not lead to the success that you desire in Advanced Placement courses. Take control of your learning.
Be safe.
Previous tests will be returned to students as soon as they are graded.
Prepare for the test. Work problems from each section. Read the chapter and section summaries. Write down what you are doing. Draw the Venn diagram or the tree diagram for complicated situations. Ask questions on the blog. Take the practice test.
Here are some answers to even HW problems:
Problem 6.10 (a) S= {all numbers between 0 and 24}
(b) = {any whole number up to and including 11,000}
(c) S = {0, 1, . . . 12}
(d) S= {any dollar and cents amount up to [insert your maximum guess here]}
(e) S = {any positive or negative number}
Problem 6.12 Four outcomes for two coins: {HH, HT, TH, TT}, eight for three coins: {HHH. HHT, HTH, HTT, THH, THT, TTH, TTT}, and sixteen for four coins (do that one yourself!).
Problem 6.16 (a) YYY -0000 through YYY-9999 = 10,000 numbers. (b) YYY-ZXX-XXXX, each X having 10 possible numbers, except the number can't start with a 0 or a 1 meaning that Z has only 8 possible values, so this means 8 * 10^6 LESS the restricted numbers (911-xxxx, 411-xxxx, etc.)
Problem 6.20 P(moves to another class) = 1 - P(stays) = 1 - .46 = .54.
Problem 6.24 P(wins large battle) = .6, P(wins three small battles) = P(wins individual small battle)^3 = .8^3 = .512. Choose the strategy with the larger probability of occurring.
Problem 6.40
Venn diagram has two circles representing getting job A and getting job B.
Both jobs: intersection of the two circles, the overlapped part, the biscuit.
First but not second: the part of circle A that is not within circle B
Second but not first: the part of circle B that is not within circle A
Neither: the part that is in the background, in NEITHER circle.
Problem 6.44
P(W) = 856/1626
P(W given prof degree) = 30/74
These are not the same. so gender and professional degree are not independent
Problem 6.56
P(y <> x) = 1/8,
P(y > x) = 1/2,
P(y <> x) = P(y <> x) /P(y > x) = 1/4.
Problem 6.48: P(W) * P(Manager given W) = P(Woman AND Manager)
One pattern that shows up a lot is Marginal * Conditional = Joint
If you divide both sides by Marginal you get
Conditional = Joint / Marginal.
IFF means IF AND ONLY IF.
IFF P(A) * P(B) = P(both A&B), A and B are independent.
IFF P(A) = P(A given B), A and B are independent.
HW for Tuesday night: DO problems 6.33 and 6.48. Read 6.66 and be prepared to work the problem. Essential question: How do mathematical independence and our regular understanding of independence relate? The chapter 4 tests were returned today. HW for Monday night: 6.39, .40, .53, and .56. The problem we worked today in class was problem .65. You would be wise to work through this problem and problem .66.
Notes from Friday (11/30) are embedded in the purple sections below.
Conditional probability rules:
PLEASE NOTE THE CORRECTION! BLOGGER WON"T ACCEPT THE VERTICAL LINE SYMBOL!!!
P(A GIVEN B) = P(A and B)/P(B)
P(B GIVEN A) = P(A and B)/P(A)
so of course
P(B) P(A GIVEN B) = P(A and B), the joint probability of A and B. It may be helpful to think of it like cancelling factors in the numerator and denominator of a fraction EXCEPT that the result is the JOINT probability. Be careful.
P(A) P(B GIVEN A) = P(A and B), again, the joint probability of A and B.
These relationships can be represented in two-way tables, Venn diagrams, and tree diagrams. The count within a cell of a two-way table divided by the marginal total is a conditional probability. Likewise, the joint probability for that cell divided by the marginal probability is also the conditional probability.
Tree diagrams can be useful when you are trying to work the problems backwards.
I don't think that I made this clear in class today:
P(A) = P(A and B) + P(A and not B) = P(A)P(B given A) + P(not A) P(B given not A).
HW for the weekend is problems 6.44 and 45.
If A and B are independent, then P(A) = P(A GIVEN B) and P(B) = P(B GIVEN A).
Interpretation: If A and B are independent, then whether or not B happened has no relationship with whether A happened.
Likewise, if A and B are independent, then whether or not A happened has no relationship with whether B happened
Today we used a Venn Diagram, a two-way table, and a tree diagram to represent the outcomes and probabilities associated with throwing two strangely-marked dice. All of the methods yielded the same answer.
HW for Tuesday (11/27) night: Re-work the weird dice problem from the AP exam (the one with two dice, one has only 9s and 0s, the other has 11s and 3s.) This time, instead of using simulation, use formal probability rules and a tree diagram, table, or Venn diagram. Answer the question in complete sentences. For part B, reconcile the answer with the joint probabilities you found in part A. Figure out the guidelines in your own words that tell you whether a price/reward is fair.
Get the reading done! What are the big concepts?
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Sorry for the delay: just got home from KSU.
HW for Monday night, Nov 26: 6.19, 20, 21
plus. . .finish State of Fear.
-----------------------------------------------------------
Add problems 6.24 and 6.25, due Monday, November 26.
Don't forget to read State of Fear.
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he complete list of HW problems due Tuesday: 6.9, 10, 12, 13, 16 (plus any others you feel like doing).
Don't forget to read State of Fear.
------------------------------------------------------------
Events that are mutually exclusive ARE NOT independent.
Addition principle: P(A or B) = P(A) + P(B) - P(A and B)
Multiplication principle: P(A) P(BA) = P(A and B), the joint probability.
When B and A are independent, P(BA) = P(B), A happening or not has not relationship to B happening, so P(A) P(B)=P(A and B). THAT IS ONLY WHEN THE EVENTS ARE INDEPENDENT.
Key vocabulary
parameter
sample space
event
probability
joint probability
independent
---------------------------------------------------------------------------
This won't be so bad. The test will be Thursday, Dec. 6.
What are YOU doing to maximize your understanding of the material?
- Are you creating an outline of the chapter?
- Have you developed a glossary for the vocabulary and formulas?
- Have you worked all of the homework problems when assigned?
- Do you read the sections that relate to the homework?
- Are you part of a study group?
- Do you ask questions?
- Have you worked problems from a study guide?
- Have you worked the online quiz (see the link on the right panel of this blog)?
- Do you look for the similarities and differences in the ways data are processed?
- Do you work with problems long enough to understand why the formulas work the way they do?
- Have you made connections between current concepts and prior knowledge?
- Have you gone online to review concepts that you have forgotten?
Just "going through the motions" does not lead to the success that you desire in Advanced Placement courses. Take control of your learning.
Be safe.
Wednesday, November 14, 2007
Chapter 5 -- Producing Data
Be sure to check the comments for this post. Your fellow classmates ask the best questions! Have you taken the online quiz? Have you worked through a study guide? Have you prepared for Thursday's test? Have you finished the reading for Tuesday? Why would I ask you to read that book in the middle of Chapter 5???? [There must be a reason.] Why would you use simulation instead of actually testing the real thing in an experiment? What are the three essential principles of good experimental design? Why is each one important? What does bias have to do with all of this? What IS bias? What IS confounding? When do you block? What is the difference between stratifying and blocking?
The two sweet diagrams of experimental design are on page 272 (Completely randomized) and page 280 (block design).
Blocking is a form of control. When a large number of your experimental units share some pre-existing condition that may make their responses to the treatment vary tremendously WITHIN the treatment groups, you will have a hard time differentiating between the results of the treatment groups. You would really prefer to have the differences in results BETWEEN groups to be big enough so you can make a decision about your comparison. To reduce this vaiability, you may choose to BLOCK by the nuisance variable (the pre-existing condition). Then you RANDOMLY allocate the experimental units in each block to the different treatments. If there are two treatments, then each block is randomly broken into two treatment groups. You proceed by running the experiment on each of the blocks individually.
Thursday and Friday (11/8-11/9) Finish writing up the experiment described below, using all the concepts of section 5.2. ALSO, answer the free response (FR) problems from 2001 and 2003 handed out in class. You definitely NEED to read the section of the book. These are NOT opinion problems.
The Chapter 5 test is Thursday, November 15. Freakonomics must be read by 11/13.
Wednesday night's (11/7) HW: 5.65 PLUS design an experiment to answer this question (at least 6-7 sentences!!).
Does the choice of presentation technology make a difference in student achievement in a geometry class?
Conditions: Geometry classes at Lassiter
four teachers teach geometry
some teachers have students write HW on the board
some teachers have students write HW answers on the overhead projector
some teachers put their official answer transparencies on the O/H.
Two document cameras are available to use (Google document camera if you haven't seen one!)
Students are already assigned to the classes.
How could we design this experiment to answer the question? What questions or clarifications do you have? Bring at least seven complete sentences of helpful guidelines for performing this study.
Friday night's HW: 5.63 and 5.64. Complete most of your Freakonomics assignment this weekend. When you get to the part where the authors belabor their unique name theory, you can consider your assignment completed. what was your favorite part? What connections did the authors make that you agree with? that you don't agree with?
Thursday night's HW: 5.60 and 5.61
Wednesday night's HW: 5.54, 5.55, 5.56 Be safe.
Tuesday night's HW: Complete both of the problems from the 2001 exam.
Example of using the TORD to simulate a bag of M&Ms with the OLD color distribution:
Old Distribution:
Brown 30%
Red 20%
Yellow 20%
Green 10%
Blue 10%
Orange 10%
Let's try this two ways. First, let's use two-digit numbers to simulate candies according to the following schedule.
01-30 Brown
31-50 Red
51-70 Yellow
71-80 Green
81-90 Blue
91-00 Orange
There are no excluded numbers. If we draw the same number twice, use it again!
Using the following line from a table of random digits, simulate drawing 5 candies.
63996 32914
63>>>>Yellow
99>>>>Orange
63>>>>Yellow
29>>>>Brown
14>>>>Brown
The second way requires only one digit. Let 1-3 represent Brown, 4-5 for Red, 6-7 for Yellow, 8 for Green, 9 for Blue, and 0 for Orange.
21833 70905
Using the TORD above, you would get
2 Brown
1 Brown
8 Green
3 Brown
3 Brown
Link to interesting site about the Dewey-Truman polling error. Did you know who the third party candidate was who threw the wrench into the process? Strom Thurmond. Your parents will be impressed that you know this.
http://www.hannibal.net/stories/101998/Pollstersrecall.html
Interesting historical link about Tukey. Scroll to the middle to see his influence in predicting outcomes of elections.
http://www.amstat.org/about/statisticians/index.cfm?fuseaction=biosinfo&BioID=14
The two books I assigned for November are Freakonomics and State of Fear. Freakonomics discusses a lot of associations/correlations that promote critical thinking. State of Fear makes you enlightened consumers of research (even though it IS fiction). Many parents have probably already read one or both of these books. Last year's students (generally) loved them.
Wednesday, October 24
Take notes on the first section of the new chapter, especially new vocabulary.
For Monday and Tuesday of next week:
5.1-5.5, 5.8, 5.11, 5.17-5.18, 5.22, 5.23
Key concepts covered in class (alliteration, anyone??) today included
undercoverage
non-response bias
response bias
convenience sampling
voluntary response sample
and examples like the C-SPAN and American Idol calls, surveying the people sitting around you, the Dewey Defeats Truman mistake, answering with un-truths, failure to respond to surveys.
Can you match the concept to the example? Can you think of another example of each concept in action? Why does each of these result in data we cannot rely on?
The two sweet diagrams of experimental design are on page 272 (Completely randomized) and page 280 (block design).
Blocking is a form of control. When a large number of your experimental units share some pre-existing condition that may make their responses to the treatment vary tremendously WITHIN the treatment groups, you will have a hard time differentiating between the results of the treatment groups. You would really prefer to have the differences in results BETWEEN groups to be big enough so you can make a decision about your comparison. To reduce this vaiability, you may choose to BLOCK by the nuisance variable (the pre-existing condition). Then you RANDOMLY allocate the experimental units in each block to the different treatments. If there are two treatments, then each block is randomly broken into two treatment groups. You proceed by running the experiment on each of the blocks individually.
Thursday and Friday (11/8-11/9) Finish writing up the experiment described below, using all the concepts of section 5.2. ALSO, answer the free response (FR) problems from 2001 and 2003 handed out in class. You definitely NEED to read the section of the book. These are NOT opinion problems.
The Chapter 5 test is Thursday, November 15. Freakonomics must be read by 11/13.
Wednesday night's (11/7) HW: 5.65 PLUS design an experiment to answer this question (at least 6-7 sentences!!).
Does the choice of presentation technology make a difference in student achievement in a geometry class?
Conditions: Geometry classes at Lassiter
four teachers teach geometry
some teachers have students write HW on the board
some teachers have students write HW answers on the overhead projector
some teachers put their official answer transparencies on the O/H.
Two document cameras are available to use (Google document camera if you haven't seen one!)
Students are already assigned to the classes.
How could we design this experiment to answer the question? What questions or clarifications do you have? Bring at least seven complete sentences of helpful guidelines for performing this study.
Friday night's HW: 5.63 and 5.64. Complete most of your Freakonomics assignment this weekend. When you get to the part where the authors belabor their unique name theory, you can consider your assignment completed. what was your favorite part? What connections did the authors make that you agree with? that you don't agree with?
Thursday night's HW: 5.60 and 5.61
Wednesday night's HW: 5.54, 5.55, 5.56 Be safe.
Tuesday night's HW: Complete both of the problems from the 2001 exam.
Example of using the TORD to simulate a bag of M&Ms with the OLD color distribution:
Old Distribution:
Brown 30%
Red 20%
Yellow 20%
Green 10%
Blue 10%
Orange 10%
Let's try this two ways. First, let's use two-digit numbers to simulate candies according to the following schedule.
01-30 Brown
31-50 Red
51-70 Yellow
71-80 Green
81-90 Blue
91-00 Orange
There are no excluded numbers. If we draw the same number twice, use it again!
Using the following line from a table of random digits, simulate drawing 5 candies.
63996 32914
63>>>>Yellow
99>>>>Orange
63>>>>Yellow
29>>>>Brown
14>>>>Brown
The second way requires only one digit. Let 1-3 represent Brown, 4-5 for Red, 6-7 for Yellow, 8 for Green, 9 for Blue, and 0 for Orange.
21833 70905
Using the TORD above, you would get
2 Brown
1 Brown
8 Green
3 Brown
3 Brown
Link to interesting site about the Dewey-Truman polling error. Did you know who the third party candidate was who threw the wrench into the process? Strom Thurmond. Your parents will be impressed that you know this.
http://www.hannibal.net/stories/101998/Pollstersrecall.html
Interesting historical link about Tukey. Scroll to the middle to see his influence in predicting outcomes of elections.
http://www.amstat.org/about/statisticians/index.cfm?fuseaction=biosinfo&BioID=14
The two books I assigned for November are Freakonomics and State of Fear. Freakonomics discusses a lot of associations/correlations that promote critical thinking. State of Fear makes you enlightened consumers of research (even though it IS fiction). Many parents have probably already read one or both of these books. Last year's students (generally) loved them.
Wednesday, October 24
Take notes on the first section of the new chapter, especially new vocabulary.
For Monday and Tuesday of next week:
5.1-5.5, 5.8, 5.11, 5.17-5.18, 5.22, 5.23
Key concepts covered in class (alliteration, anyone??) today included
undercoverage
non-response bias
response bias
convenience sampling
voluntary response sample
and examples like the C-SPAN and American Idol calls, surveying the people sitting around you, the Dewey Defeats Truman mistake, answering with un-truths, failure to respond to surveys.
Can you match the concept to the example? Can you think of another example of each concept in action? Why does each of these result in data we cannot rely on?
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