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Solved: “Made in the USA” survey. Refer to the Journal of
Chapter 10, Problem 41SE(choose chapter or problem)
“Made in the USA” survey. Refer to the Journal of Global Business (Spring 2002) study of what “Made in the USA” on product labels means to the typical consumer, Exercise 2.152 (p. 116). 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. 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% 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 \(p_1\), \(p_2\), \(p_3\), and \(p_4\), 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 \(\alpha\ =\ .10\).
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.
Questions & Answers
QUESTION:
“Made in the USA” survey. Refer to the Journal of Global Business (Spring 2002) study of what “Made in the USA” on product labels means to the typical consumer, Exercise 2.152 (p. 116). 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. 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% 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 \(p_1\), \(p_2\), \(p_3\), and \(p_4\), 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 \(\alpha\ =\ .10\).
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.
ANSWER:Step 1 of 9
(a)
Qualitative variable:
All the levels of the responses to “Made in the USA” are considered as the qualitative variable.
That is, the levels 100%, 75% to 99%, 50% to 74%, and less than 50% are the qualitative variables associated with the study.