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.

4. A problem with a cell phone that prevents a customer from receiving calls is upsetting both customers and the telecommunications company. The file Phone contains samples of 20 problems reported to two different offices of the telecommunication company and the time to clear these problems (in minutes) from the customers’ phones. Is there evidence that addressing this phone issue results in different mean waiting times at the two offices? (Use a 0.05 level of significance)

Time	Location
8.72	1
6.66	1
2.66	1
3.67	1
7.44	1
6.87	1
6.87	1
8.86	1
2.09	1
1.86	1
1.60	1
2.12	1
2.69	1
4.45	1
0.37	1
2.83	1
3.01	1
5.26	1
3.14	1
5.76	1
1.14	2
2.23	2
2.67	2
4.08	2
2.42	2
1.48	2
3.19	2
2.91	2
0.76	2
2.90	2
1.74	2
0.64	2
1.51	2
0.87	2
2.24	2
4.39	2
3.76	2
1.82	2
2.23	2
2.61	2

Answer 1

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

We have to assume unequal-variances for this t-test becuase the standard deviation of Location 1 is more than twice of the Location 2.

Location	N	Mean	StDev	SE Mean
1	20	4.35	2.53	0.56
2	20	2.28	1.07	0.24

The output is:

The p-value is 0.002.

Since the p-value (0.002) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that addressing this phone issue results in different mean waiting times at the two offices.