AP StatisticsName: ______

Chapter 11 Extra Practice Answers

Use the following information for numbers 1 – 6:

A large company planning to install drink vending machines in its office building selectssimple random samples of both the professional staff and the administrative support staff andasks people to choose between two brands of drink machines—Coca-Cola or Pepsi. Here arethe results.

Drink Brand / Professional Staff / Support Staff / Total
Coca-cola / 14 / 30 / 44
Pepsi / 8 / 43 / 51
Total / 22 / 73 / 95

1. Which of the following is the appropriate type of significance test that should be used to decide whether these data provide convincing evidence that there is a difference in the brand preferences of theprofessional and administrative support staffs?

a) Chi-Square Goodness of Fit Testb) Chi-Square Test for Homogeneity

c) Two-Sample z Test for a Difference between Two Proportionsd) Chi-Square Test for Association/Independence

e) One-Sample z Test for a Population Proportion

2. State the appropriate null and alternative hypotheses for the test that will address this question.

H0: The distribution of drink brand preference is thesame for both the professional and support staffs.

Ha: The distribution of drink brand preference is different for both the professional and support staffs.

3. Find the expected counts for each category under the assumption that the null hypothesis is true.

Professional Staff / Support Staff
Coca-cola / 10.2 / 33.8
Pepsi / 11.8 / 39.2

For the next three problems, assume that all of the conditions have been met.

4. Calculate the value of the χ2 test statistic.

χ2 =

χ2 = 3.454

5. Determine the P-value of the test.

P(χ>3.45) = 0.0631, df = (2-1)(2-1) = 1

6. State your conclusion.

Fail to reject H0. Since the P-value, 0.0631, is greater than  = 0.05, there is not enough evidence to suggest that the distribution of drink brand preference is different for the professional and support staffs.