Number of Sales on Wed for 8 Weeks Wed with Sign Wed without Sign 7 6. 8. 11 a.) Did customers make a different amount of purchases when the signs were displayed? Carry out a t-test for independent means (use the .05 significance level). Use the five steps of hypothesis testing. Label all the steps clearly. Show ALL Work/calculations.

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**Title: Examining the Impact of Signage on Store Sales**

A manager of a small store wanted to discourage shoplifters by putting signs around the store that said, "Shoplifting is a crime!"; while at the same time making sure the signs would not affect the number of sales. To test the effect on sales, the signs were displayed every other Wednesday for 8 weeks, and the numbers of sales for those four Wednesdays were recorded. The numbers of sales for the four alternate Wednesdays without the sign are also listed in the table below. Here are the results:

**Number of Sales on Wednesday for 8 Weeks**

| Wed with Sign | Wed without Sign |
|---------------|------------------|
| 7             | 9                |
| 8             | 8                |
| 7             | 11               |
| 9             | 7                |

**Analysis Tasks:**

a.) Did customers make a different amount of purchases when the signs were displayed? Carry out a t-test for independent means. Use the .05 significance level. Use the five steps of hypothesis testing. Label all the steps clearly. Show all work/calculations.

b.) Report the statistic in APA format (the statistical sentence).

**Graph/Diagram Explanation:**

This table compares the number of sales on Wednesdays when the "Shoplifting is a crime!" signs were present versus when they were not. It highlights a potential difference in customer purchase behavior between the two conditions. The comparison will be statistically analyzed using an independent t-test to determine if the signage caused a significant effect on sales figures.
Transcribed Image Text:**Title: Examining the Impact of Signage on Store Sales** A manager of a small store wanted to discourage shoplifters by putting signs around the store that said, "Shoplifting is a crime!"; while at the same time making sure the signs would not affect the number of sales. To test the effect on sales, the signs were displayed every other Wednesday for 8 weeks, and the numbers of sales for those four Wednesdays were recorded. The numbers of sales for the four alternate Wednesdays without the sign are also listed in the table below. Here are the results: **Number of Sales on Wednesday for 8 Weeks** | Wed with Sign | Wed without Sign | |---------------|------------------| | 7 | 9 | | 8 | 8 | | 7 | 11 | | 9 | 7 | **Analysis Tasks:** a.) Did customers make a different amount of purchases when the signs were displayed? Carry out a t-test for independent means. Use the .05 significance level. Use the five steps of hypothesis testing. Label all the steps clearly. Show all work/calculations. b.) Report the statistic in APA format (the statistical sentence). **Graph/Diagram Explanation:** This table compares the number of sales on Wednesdays when the "Shoplifting is a crime!" signs were present versus when they were not. It highlights a potential difference in customer purchase behavior between the two conditions. The comparison will be statistically analyzed using an independent t-test to determine if the signage caused a significant effect on sales figures.
Expert Solution
Step 1

Independent t test is given by;

t=(D)ND2-(D)2N(N-1)N

where

  • D is sum of differences
  • D2 is the sum of squared differences
  • N is the number of observations

Null and alternative hypothesis will be;

H0: Means are equal(μ1=μ2)

H1: Means are not equal(μ1μ2)

 

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