Question

Do consumers spend more on a trip to Store A or Store​ B? Suppose researchers interested in this question collected a systematic sample from 82 Store A customers and 80 Store B customers by asking customers for their purchase amount as they left the stores. The data collected is summarized by the accompanying table. Suppose researchers decide to test the hypothesis that the means are equal. The degrees of freedom formula gives 157.41 df. Test the null hypothesis at alpha=0.05.

	Store A	Store B
n	82	80
y overbary	41	51
s	21	18

Compute the test statistic.

t=?

Find the​ P-value.

The​ P-value is__?

State the conclusion. Choose the correct answer below.

A. Reject the null hypothesis. There is not sufficient evidence that the means are not equal.

B. Fail to reject the null hypothesis. There is not sufficient evidence that the means are not equal.

C. Fail to reject the null hypothesis. There is sufficient evidence that the means are not equal.

D. Reject the null hypothesis. There is sufficient evidence that the means are not equal.

Answer 1

Given that,

For store A : n1 = 82, y1-bar = 41 and s1 = 21

For store B : n2 = 80, y2-bar = 51 and s2 = 18

The null and alternative hypotheses are,

H0 : μ1 = μ2

Ha : μ1 ≠ μ2

Test statistic is,

=> Test statistic = -3.257

Degrees of freedom = 157.41 ≈ 157

Using Excel we find, p-value :

Excel Command : =TDIST (3.257, 157, 2) = 0.0014

=> P-value = 0.0014

Simce, p-value is less than significance level of 0.05, we reject the null hypothesis.

Conclusion : Reject the null hypothesis. There is sufficient evidence that the means are not equal.

Answer : D)