Second semester 2011--Starting with chapter 9&10

Welcome back, students!

AP REGISTRATION LINK: https://user.totalregistration.net/AP/111983
PLEASE LET YOUR TEACHER KNOW IF FINANCIAL HARDSHIP PREVENTS YOU FROM REGISTERING. WE'LL TRY TO FIND A WAY TO SOLVE THE ISSUE.

We begin by investigating the distributions of p-hat and x-bar. This is the concept of sampling distributions. We consider the distribution of ALL the sample means that we would observe if we took EVERY sample of size n from a population.

In class on Wednesday we collected data: we computed average penny ages from samples of sizes 5, 10, and 25. We have more collecting and computing to do before the distributions become evident from the graphs. Prepare to crank through more pennies on Thursday. (The program we used to report the findings is Fathom.)

Homework January 4th: Work one problem from the handout completely. Become a master of that problem.

Homework January 5th: Read pages 563-568 from the text and work problems 9.1, 9.2, and 9.5.

Be prepared for a quiz at any time.

Homework January 7th: Problem 9.7 using Excel if possible, problems 9.10 through 9.17.
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Homework January 20: Problems 9.31, 9.32, 9.33 HAVE THIS DONE BY MONDAY. Remember, your book should be read by Wednesday.

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February 9, 2011
You've been busy in class collecting data and constructing confidence intervals for the mean and for the proportion.
There are three cases to consider on tomorrow's test:

Confidence intervals for proportions
Check n phat and n(1-phat) and that n < 1/0 N
Use the sample proportion (phat) in your calculation of the standard error
Use a Z statistic for computing the margin of error
Don't forget the interpretation

Confidence intervals for the mean (when we miraculously KNOW the population standard deviation)
Check that the observed values would not indicate that the means would be non-normal
Are the observations random and independent?
Use the CLT--standard error = pop std dev / sqrt sample size
Use Z (remember, this is the miraculous case)
Don't forget the interpretation

Confidence intervals for the mean (when we miraculously DON'T KNOW the population standard deviation)
Check that the observed values would not indicate that the means would be non-normal
Are the observations random and independent?
Use the CLT--standard error = SAMPLE std dev / sqrt sample size
Use t-distribution with n-1 degrees of freedom
Don't forget the interpretation

Margin of error = (Z or t)* Std error
Greater confidence = wider margin of error
Larger sample size = smaller margin of error

Good interpretation of the confidence interval:
We are 95% confident that the true population mean test score falls between 3.2 and 3.6.

Good interpretation of the confidence level:
If this procedure were repeated many times, we would expect approximately 95% of the confidence intervals constructed from the sample mean test scores to contain the true population mean test score.

Bad interpretations:
Like you really expected me to post BAD examples? Anything that says there is a 95% chance. . . is really bad.

A confidence interval without an interpretation is relatively worthless. Almost as bad as using a point estimate instead of a confidence interval! Don't fall into the lazy trap of answering questions without including all the required parts.