Refer to the Journal of Global Business (Spring 2002) study of what "Made in the USA" on product labels means to the typical consumer, presented in Exercise 2.179 (p. 99). Recall that 106 shoppers participated in the survey. Their responses, given as a percentage of U.S. labor and materials in four categories, are summarized as follows: 64 shoppers responded 100%; 20 shoppers stated 75 to 99%; 18 shoppers stated 50 to 74%; and 4 shoppers said less than 50%. Suppose a consumer advocate group claims that half of all consumers believe that
"Made in the USA" means "100%" of labor and materials are produced in the United States, one-fourth believe that "75 to 99%" are produced in the United States, one fifth believe that "50 to 74%" are produced in the United States, and 5 percent believe that "less than 50%" are produced in the United States.
a. Describe the qualitative variable of interest in the study. Give the levels (categories) associated with the variable.
b. What are the values of p1, p2, p3, and p4, the probabilities associated with the four response categories hypothesized by the consumer advocate group?
c. Give the null and alternative hypotheses for testing the consumer advocate group's claim.
d. Compute the test statistic for testing the hypotheses stated in part c.
e. Find the rejection region of the test at a = .10.
f. State the conclusion in the words of the problem.
g. Find and interpret a 90% confidence interval for the true proportion of consumers who believe that "Made in the USA" means that "100%" of labor and materials are produced in the United States.