# “Made in the USA” survey. 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 in the table. uppose 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% believe that “less than 50%” are produced in the United States. Response to “Made in the USA” 100% 75% to 99% 50% to 74% Less than 50% Number of shoppers 64 20 18 4 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, 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 “Made in the USA” means “100%” of labor and materials are produced in the United States.

“Made in the USA” survey. 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 in the table.  uppose 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% believe that “less than 50%” are produced in the United States.
Response to “Made in the USA”
100%
75% to 99%
50% to 74%
Less than 50%

Number of shoppers
64
20
18
4

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, 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 “Made in the USA” means “100%” of labor and materials are produced in the United States.