Question

A company that owns a grocery market chain wants to know if their new country theme will encourage shoppers to spend more time in their markets shopping and hopefully increase overall market sales. Previous research from ten years ago found that the average shopper spent $65.00 at their markets. Ten of the company’s 100 stores were randomly selected and remodeled in the new country theme. Fifteen shoppers at these new country theme stores were randomly selected and the amount of their shopping bill was recorded. The shopping totals for the 15 shoppers is given below:

Bill Total $

$61

$72

$68

$64

$83

$77

$72

$76

$74

$68

$81

$80

$70

$75

$79

A. What is the null hypothesis for this problem?

E. Conduct a test of the null hypothesis at p = .05. Be sure to properly state your statistical conclusion (i.e., “Since t = _______, p <> .05; Reject or Fail to reject the null hypothesis”) F. Provide an interpretation of your statistical conclusion. G. What type of statistical error might you have made in part F?

Answer 1

A. Here the null hypothesis is

c9 = 11: 'H

and the alternative hypothesis is

9 <11:11

The rest is done using MINITAB 2017.

One-Sample T: X

Test of μ = 65 vs > 65

Variable N Mean StDev SE Mean 95% Lower Bound T P
X 15 73.33 6.34 1.64 70.45 5.09 0.000

E. As the p-value is less than 0.05, the null hypothesis is rejected at 5% level of significance.

F. Hence it can be concluded that overall market sales has actually increased at 5% level of significance.

G. As here the decision is to reject the null hypothesis, type I error may be committed in rejecting the null which is true.