Question

Do consumers spend more on a trip to Target compared to Walmart? Suppose researchers interested in this question collected a random sample from 80 Target customers and 85 Walmart customers by asking customers for their purchase amount as they left the stores. The 80 Target customers have the mean purchase amount $53 and the standard deviation $19. The 85 Walmart customers have the mean purchase amount $45 and the standard deviation $21.

1. [2 points] Is the data collected from independent samples or dependent samples?

2. [2 points] Is the relevant test statistic z-stat or t-stat?

3. [4 points] Write down the hypotheses of the test.

4. [4 points] The p-value is calculated to be 0.0056. Write down the conclusion of the test. Assume an α=0.05 level of significance.

Answer 1

a) the data collected from independent samples

b) the relevant test statistic or t-stat

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Now, the value of test static can be found out by following formula:

d)

Using Excel's function =T.DIST.RT(t0,n-1), the P-value for t0 = 2.5607 in an upper-tailed t-test with 163 degrees of freedom can be computed as

Since P = 0.0056 < 0.05, we reject the null hypothesis

Conclusion: We have sufficient evidence to claim that consumers spend more on a trip to Target compared to Walmart