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)?
Subscribe to:
Posts (Atom)
Posts
