10.1 Classwork AP Statistics Name

10.1 Classwork AP Statistics Name:

Suppose you administer a certain aptitude test to a random sample of 9 students in your school, and that the average score is 105. We want to determine the mean µ of the population of all students in the school. Assume a standard deviation of s = 15 for the test.

1. What is the upper critical value for a 98% confidence interval? (Show the key numbers in the sketch of the distribution.)

2. Explain the meaning of “98% confident.”

3. What is the standard deviation of the mean, ?

4. Calculate a 98% confidence interval for the mean score µ for the whole school. Follow the Inference Toolbox.

5. What sample size would be needed to have a margin of error at most 4 points?

Suppose your class is investigating the weights of Snickers 1-ounce fun-size candy bars to see if customers are getting full value for their money. Assume that the weights are normally distributed with standard deviation s = .005 ounces. Several candy bars are randomly selected and weighed with sensitive balances borrowed from the physics lab. The weights are:

.95 1.02 .98 .97 1.05 1.01 .98 1.00

ounces. We want to determine a 90% confidence interval for the true mean, µ.

6. What is the sample mean?

7. Explain the meaning of the confidence level.

8. Determine z*. (Show work, including a sketch of the distribution.)

9. Find the margin of error.

10. Determine the 90% confidence interval for the mean weight of the candy bars. Follow the Inference Toolbox.

From a population with standard deviation 25, a sample of size 100 is drawn. The mean of the sample is 235.

11. Find z* for a 90% confidence interval for the true mean of the population. Show your work using the graph provided.

12. Construct a 90% confidence interval for . Follow the Inference Toolbox.

13. Joey says that 90% of the observations are in this interval. Is Joey right? If not, what is the proper interpretation of this 90% confidence interval?

14. An evaluator wishes to make a statement about the emotional maturity of the freshman population at your school, so she decides to sample the population and administer an emotional maturity test. Putting aside any concerns about the validity of the test used, and considering sampling techniques only, how many students should she sample in order to be 95% confident that her estimate of freshman emotional maturity will be within 6 units of the true mean? (The test publishers indicate the population variance is 100 units.)

Chapter 10