A manager of a small store wanted to discourage shoplifters

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 this would not result in customers buying less. To test this, 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 customers buy less when the signs are displayed? (Use the .05 significance level.)

a.     Use the five steps of hypothesis testing.

b.     Sketch the distribution involved.

c.     Figure the effect size.

d.     Explain what you did to a person who is familiar with the t test for a single sample but is unfamiliar with the t test for independent means.

PLEASE EXPLAIN THE PROCESS. I AM REALLY LOST.

Solution

Null Hypothesis: Mu(With sign) < Mu(Without Sign)

Alternate Hypothesis : Mu(With sign) >= Mu(Without Sign)

Data1 : { 83, 73, 81, 79 }

Mean1 = 79

SD1 = 4.32

n1 = 4

Data2 : {84, 90, 82, 84}

Mean2 =85

SD2 =3.46

n2=4

Standard Error : = sqrt((4.32^2/4) + (3.46^2/4)) = 2.767

t = (79 -85) / 2.767 = -2.168

dF = 4+4 -2 = 6

P-value = 0.036

Since , P-value < 0.05

Reject null hypothesis.