A supermarket chain wants to know if their “buy one, get one free” campaign incr

Question

A supermarket chain wants to know if their “buy one, get one free” campaign increases customer traffic enough to justify the cost of the program. For each of 10 stores they select two days at random to run the test. For one of those days (selected by a coin flip), the program will be in effect. They want to determine whether the program increases the mean traffic. The results in number of customer visits to the 10 stores are in the data set.

Answer each of the questions below using hypothesis testing. Follow the seven-step procedure for testing a hypothesis in your text book as a guide for answering the questions. Use a .05 significance level.

1. Previous data suggests mean store traffic is 145. Is the mean traffic without the program different from 145?

2. Is the mean traffic with the program greater than 145?

3. Did the program increase store traffic? Use a pooled t-test.

4. Did the program increase store traffic? Use a paired difference t-test.

Turn in your findings as described below. Generally the report will be graded for clarity (how easy it is to understand you), completeness (no significant gaps in the information provided) and correctness (the values and descriptions are correct). The report will also be graded on adherence to the report standard. The report will be structured as follows

Section 1: For each question, provide

• The null hypothesis

• The alternate hypothesis

• The test statistic chosen (including which test)

• The critical value and decision rule

• The P-value

• Your findings

Section 2: Questions 3 and 4 ask for two different approaches to the same question. The results differ. Write a paragraph describing which approach is the most appropriate. You should end with a clear (yes-no) conclusion to the question.

DATA:

Store # With Program Without Program 1 140 136 2 233 235 3 110 108 4 42 35 5 332 328 6 135 135 7 151 144 8 33 39 9 178 170 10 147 141

Explanation / Answer

1. Using Minitab

Descriptive Statistics: With Program, Without Program

Variable Mean
With Program 150.1
Without Program 147.1

2.Yes,

The mean traffic with the program greater than 145/

3.

H0 (the null hypothesis): That the difference, mA - mB , is equal to the chosen reference value (usually zero)

·    H1 (the alternative hypothesis): That mA - mB is not equal to the chosen reference value.

Two-Sample T-Test and CI: With Program, Without Program

Two-sample T for With Program vs Without Program

SE
N Mean StDev Mean
With Program 10 150.1 87.0 28
Without Program 10 147.1 86.3 27

Difference = (With Program) - (Without Program)
Estimate for difference: 3.0
95% CI for difference: (-78.4, 84.4)
T-Test of difference = 0 (vs ): T-Value = 0.08 P-Value = 0.939 DF = 18
Both use Pooled StDev = 86.6531

Conclusion:

the t-value is 0.08 and the associated p-value is 0.939. When Minitab displays a p-value of 0.939 it means that the actual p-value is greater than 0.05. This p-value indicates that there is greater than a 0.05% chance that you would have obtained your samples if mA - mB was actually not 0.

4.

Paired T-Test and CI: With Program, Without Program

Paired T for With Program - Without Program

N Mean StDev SE Mean
With Program 10 150.1 87.0 27.5
Without Program 10 147.1 86.3 27.3
Difference 10 3.00 4.52 1.43

95% CI for mean difference: (-0.23, 6.23)
T-Test of mean difference = 0 (vs 0): T-Value = 2.10 P-Value = 0.065

t-value is 2.10, and the associated p-value is 0.017. A p-value of 0.065 indicates that there is only a 6.5% chance that you would have obtained your sample difference if m D was actually not 0.

Hope this will be helpful,Thanks :-)

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