Use the “Project 2 data” data set. You may use Excel to help you with the statis

Question

Use the “Project 2 data” data set. You may use Excel to help you with the statistical analysis.

Abstract: 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

Question-1

Step-1 Null hypothesis H0 : µ=145

Step-2Alternative hypothesis Ha : µ145

Step-3 Level of significance chosen is 0.05

For this we will use one-sample t-test with test statistic t following student’s t-distribution with degrees of freedom =n-1

Sample size n=10

Degree of freedom=n-1=10-1=9

Critical t=±2.262

Step-4

We reject the null hypothesis if calculated t<-2.262 or >2.262

Step-5

From following results xbar=147.10 and s=86.33

So test statistic t=(xbar-145)/(s/sqrt(n))

=(147.10-145)/(86.33/sqrt(10))

=0.0769

Step-6: p-value=tdist(0.0769,9,2)=0.9404

Step-7 As p-value.0.05 and t<2.262, we do not reject the null hypothesis and conclude that the mean traffic without the program is not different from 145?

Store #

Without Program

1

136

2

235

3

108

4

35

5

328

6

135

7

144

8

39

9

170

10

141

Mean xbar

147.10

Standard deviation s

86.33

Store #

Without Program

1

136

2

235

3

108

4

35

5

328

6

135

7

144

8

39

9

170

10

141

Mean xbar

147.10

Standard deviation s

86.33

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