Question

5. Hypothesis testing

Consumer data collected from shopper cards show that, nationwide, 87% of U.S. shoppers hoard buy toilet paper. A grocery store manager thinks that more than 95% of shoppers at his store hoard buy toilet paper. He takes a random sample of 500 shoppers and finds that 459 purchased toilet paper.

a. What are the hypotheses?

b. Assume alpha is 0.05. What is the test statistic? What is the value of the test statistic?

c. What is the p-value?

d. What is the conclusion?

Answer 1

Solution :

a) This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.95

Ha : p > 0.95

= x / n = 459/500 = 0.918

P0 = 0.95

1 - P0 = 1-0.95 =0.05

b) Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.918 -0.95 / [.95*(0.05) /500 ]

= -3.283

P(z < -3.283) = 0.9995

c) P-value = 0.9995

= 0.05    

The critical value for a right-tailed test is zc​=1.64.

0.9995 > 0.05

Fail to reject the null hypothesis .

d) There is insufficient evidence to suggest that the population proportion pp is greater than 95%​, at α=0.05 significance level.