Question

6. A manager of a small store wanted to discourage shoplifters by putting signs around the store saying: “Shoplifting is a

crime!” However, he wanted to make sure that this sign would work. To test his research hypothesis that customers would actually buy more) , he displayed the signs every other Wednesday for 8 weeks, for a total of 4 days displayed. He recorded the store’s sales for those four Wednesdays, and then recorded the store’s sales for the four alternate Wednesdays, when the signs were not displayed. On the Wednesdays with the sign, the sales were 83, 73, 81, and 79. On the Wednesdays without the sign, sales were 84, 90, 82, and 84. Do these results suggest that the general population of customers buy more when the signs are displayed? Use the .05 significance level. Note: Pay attention to the wording in this question when formulating your hypotheses and conclusions!

a) Use the four steps of hypothesis testing
b) Illustrate the distributions involved
c) Calculate the effect size of this study (can use Cohen’s d or r2)

Answer 1

The hypothesis being tested is:

The null hypothesis: The general population of customers buy the same when the signs are displayed

The alternative hypothesis: The general population of customers buy more when the signs are displayed

The output is:

79.000	mean With the Sign
85.000	mean Without the Sign
-6.000	mean difference (With the Sign - Without the Sign)
7.572	std. dev.
3.786	std. error
4	n
3	df
0.79	Cohen’s d
-1.585	t
.1056	p-value (one-tailed, lower)

Since the p-value (0.1056) is greater than the significance level, we cannot reject the null hypothesis.

Therefore, we cannot conclude that the general population of customers buy more when the signs are displayed.

The effect size is 0.79.