Question

For each of the following two-samples t-tests (problems 1-6): (a) Determine if a F test for the ratio of two variances is appropriate to calculate for the context. If it is appropriate, conduct the analysis and report the result. Include what statistical conclusion you should draw from the analysis (i.e., whether you should conduct a pooled-variance t-test or an unequal-variances t-test). (b) Identify the most appropriate t-test to conduct for the situation/data given. Don’t forget to consider if the context requires one/two-tail tests. (c) Provide a statistical and practical interpretation of your findings.

6. Target versus Walmart: Who had the lowest prices? To address your consumer thirst for knowledge you identify 20 items (all brand-name items) currently on your household shopping list. You visit both your Local Target and Walmart, price each item, organize, and then store these data in TargetWalmart. Is there evidence to support that prices are cheaper at Walmart? (Use a 0.05 level of significance)

Shopping Item	Target	Walmart
1	3.29	3.77
2	23.79	24.52
3	1.09	1.64
4	23.39	24.18
5	11.89	12.06
6	7.09	8.01
7	19.09	19.22
8	2.29	2.02
9	10.49	11.16
10	2.29	2.55
11	2.99	2.43
12	21.09	20.69
13	4.49	3.88
14	7.09	6.23
15	5.39	5.21
16	10.29	10.51
17	2.49	3.31
18	1.19	1.18
19	3.29	4.06
20	3.69	4.21

Answer 1

(a) Determine if an F test for the ratio of two variances is appropriate to calculate for the context. If it is appropriate, conduct the analysis and report the result. Include what statistical conclusion you should draw from the analysis (i.e., whether you should conduct a pooled-variance t-test or an unequal-variances t-test).

Ans: F test generally used to test whether at least two means of the groups are the same or not when the number of the groups is more than 2. It can use when the number of groups is equal to 2. So, F test for the ratio of two variances is appropriate to calculate for the context.

The p-value is 0.932 and more than 0.05 level of significance. Hence, we can conclude that the mean price between Target and Walmart are the same.

We should conduct a pooled-variance t-test because the standard deviations of the two locations is not different.

(b) Identify the most appropriate t-test to conduct for the situation/data given. Don’t forget to consider if the context requires one/two-tail tests.

Ans: The most appropriate test is t-test with two tail for the given data.

The p-value is 0.534 and greater than 0.05 level of significance. Hence, we can conclude that the mean price between Target and Walmart is the same.

(c) Provide a statistical and practical interpretation of your findings.

Ans: Hypothesis

Ho: The mean price of Target and Walmart is the same.

H1: The mean price of Target and Walmart is not the same.

Statistical: We do not reject the null hypothesis.

Practical interpretation: We can conclude that the mean price between Target and Walmart is the same.

6. Target versus Walmart: Who had the lowest prices? To address your consumer thirst for knowledge you identify 20 items (all brand-name items) currently on your household shopping list. You visit both your Local Target and Walmart, price each item, organize, and then store these data in TargetWalmart. Is there evidence to support that prices are cheaper at Walmart? (Use a 0.05 level of significance)

Ans: From b, the mean price of Target and Walmart are  8.33 and 8.54 respectively. In terms of value, Walmart has a lower mean value. But, it required a statistical test.

The p-value is 0.466 and greater than 0.05 level of significance. Hence, we can conclude that the mean price of Target does not less than Walmart.