Question

Most people have returned clothing or other items to stores. Acme holding company is particularly interested in the clothes that have been returned after the winter holidays. It requires its stores to keep records of these clothes if they cost over $75.00. Acme’s corporate office is worried about a new store (N) it recently purchased. The store seems to have a high proportion of returns compared to an established store (E) in a similar neighborhood. After the last holiday season, store N had 162 returns of clothing items that cost over $75. In total store N sold 900 items. Store (E) had 60 returns that cost over $75 out of total sales of 750 items. (Assume that these are a random sample of all returns after the winter holidays from both stores.) Acme wants to check whether the new store has a significantly higher proportion of returns than the established store.

a. State the null and alternative hypotheses.

b. Will you perform a left-tailed, right-tailed, or two-tailed test?

c. Calculate the sample proportions for both populations.

d. Compute the pooled proportion.

e. Calculate the standard error of the differences.

f.  Compute the difference of the sample proportions (p1−p2).

g.  Calculate the test statistic (Z-score).

h. Is the test statistic unusual? Why or why not?

i. Find the p-value.

j. What can you conclude about the null hypothesis (reject the null or fail to reject the null)?

k. Interpret your conclusion in the context of this problem.

Answer 1

Given:

For store N :

Number of clothing items = X1 = 162

Total number of clothing items = n1 = 900

For store E :

Number of clothing items = X2 = 60

Total number of clothing items = n2 = 750

Claim : The store N seems to have a high proportion of returns compared to an established store (E) in a similar neighborhood.

a) Hypothesis test:

The null and alternative hypothesis is

Ho : p1 p2

Ha : p1 > p2

b) Since alternative hypothesis contain > sign, this a right-tailed test.

Since P-value is less than significance level 0.05, we reject null hypothesis.

Reject the null.

Conclusion: There is sufficient evidence to conclude that the store N seems to have a high proportion of returns compared to an established store (E) in a similar neighborhood.