Question

Part 2: T-tests and Correlation

For each question, conduct the appropriate statistical analysis. If some sort of t-test is appropriate for the question, determine which type of t-test is appropriate. If you are going to conduct an independent samples t-test, determine whether you need to do the version of the test for equal variances or the version for unequal variances. For each test, state the null hypothesis, state the alternative hypothesis, state the type of test that you conducted, and report and interpret the results. If ANOVA is the appropriate analysis, follow-up with the appropriate post-hoc tests if you reject the null hypothesis for your ANOVA. The data for each question can be found in the Excel file entitled “Data for Project 3.” Show your work in your spreadsheet just as you did for the practice exercise. Each question is worth 7 points.

A group of 12 welfare recipients participated in a job training program. Before- and after-abilities were measured through a standardized test. The data can be found in the sheet entitled “Part 2 Question 1.” Is there evidence of improvement?

Before	After
5	7
4	5
6	6
4	5
5	5
4	5
3	4
6	5
5	5
4	5
4	4
5	6

An important function of a firm’s human resources manager is to track worker turnover. As a general rule, companies prefer to retain workers. New workers frequently need to be trained and it often takes time for new workers to learn how to perform their jobs. To investigate nationwide results, a human resources manager organized a survey wherein a random sample of men and women was asked how many years they had worked for their current employers. The data can be found in the sheet entitled “Part 2 Question 2”. Can we infer that men and women have different job tenures?

Men	Women
3.2	0.7
15.7	0.9
1.3	0.8
0.7	0.3
8.6	5.8
10.4	2.3
3.2	1.4
1.3	9.3
23.9	5.7
0.2	12.1
0.8	2.8
11.1	0.4
1.5	1.4
3.7	1
14.9	0.8
3	11.9
2.3	4.8
18.2	1.3
12.9	21.5
2.5	10.8
3.8	6.3
3.4	20.7
5.5	1.8
3.8	16.4
7.3	4.1
3.7	2.7
9.7	1.4
10.3	20.7
4.3	4.5
9	4
15.8	0.6
9.9	3
4.1	1.1
5.6	7
1.4	1.4
0.1	2.3
1.2	17
5.1	6
5.8	3.7
6.8	6.8
13.7	6.1
6.1	0.4
6.4	4.9
2.5	3.3
2.2	10.6
4.4	4.9
18.1	0.3
0.4	4.7
2.8	3.7
13.9	1.4
7.9	2.8
5.4	1.3
6.2	18.6
2.5	4
1.3	7.1
10	2.5
2	30.8
1.5	5.8
4.3	8.9
1.3	7.6
5.8	11.2
2.8	3.2
1.5	9.4
0.6	5.6
5.8	8.2
4.8	0.1
2.7	2.5
5.7	11.1
17	2.8
11.3	1.1
9.6	13.5
1.9	2.2
15.8	10.3
2.4	1.6
5.6	6.6
0.9	1.9
0.6	1.3
11.2	1.7
0.6	7.8
1.2	5.3
0.7	3.1
3.1	5.2
0.2	7.6
0.5	0.6
3.7	5.6
7.1	2.2
1.6	10.5
0.1	2.8
3.8	8.5
3.6	6.2
1.8	18.3
1.4	3.4
11.3	8.9
10.2	20.2
1.6	0.6
1	2.5
5.3	3
10.1	0.7
3.4	10.7
3.7	0.3
6.4	4.1
14.2	35.9
2.2	7.1
2.6	4.2
18.9	3.2
6.4	1.4
12	2
6.6	2
7.3	20.9
5.3	25.2
10.3	1.4
16.7	5.2
12.6	2.9
1.9	3
7.1	2.5
6.6	6.1
1.6	12.4
3.2	3
1.6	8.4
0.9	0.8
0.5	13
1.5	1.5
1.9	1.1
4.8	5.9
18	8.4
1	10.6
0.8	4.2
16.5	0.6
1.6	17.6
3.1	1.4
0.6	4.7
10.8	15.4
1.2	8.6
3.1	2.6
3.3	0.6
3.1	8.8
3.7	5.6
0.7	10.3
2.5	6.5
2.3	1.6
5	0.6
0.3	0.8
4.1	7.9
3.4	3.5
6.2	7.5
8	6.5
7.8	3.3
1.8	3.2
0.3	2.4
0.7	3.3
14.1	3.6
5.1	8.1
2.5	3.9
3.3	1
1.5	2
19.5	27.9
3	15.4
1.8	0.5
3	0.5
14.7	3.2
21.4	2
11.8	18.5
8	2.9
0.9	1.2
23.5	5
4.7	1.4
4	11.5
3.3	10.8
3.3	0.9
16.6	0.5
1.6	2.2
0.6	14.9
6.3	0.4
13.4	5.4
1.1	4.5
2.6	0.8
11.2	0.1
5	7.2
17.3	3.2
0.2	6.3
4	7.3
5.2	3
8	17.9
12.2	0.1
0.7	8.9
3.4	0.1
0.4	2.3
1.3	12
0.8	3.5
3.2	1.4
1.2	2.7
1.6	9.9
15	0.9
11.7	2.4
6.6	3.1
5.3	2.2
9.5	10.7
1.4	10.7
5.9	15.7
9.1	4.5
2.1	3.5
0.6	4.9
1.6	5.9
1	4.6
1.8	7.6
29.3	2
6	4.1
16.4	0.5
8	12
2.6	1.4
13.6	16.2
1.1	0.8
4.5	5.4
1.6	0.1
5.8	1.1
0.2	8.6
3	1.7
0.1	3.4
2.8	1.3
11	2.8
4.9	1.7
24.1	5.3
15	0.2
6.1	2.6
9.3	1.1
1	7.1
1.5	5.3
1	2.5
2.5	20.3
0.5	7
0.2	0.4
2.3	2.2
0.4	3.1
10.9	7.5
8.3	1.2
5.3	6.6
1.4	10.1
2.5	2.8
2.5	1.7
2	18.8
1.2	3
3.3	1.6
2.9	1.5
1.8	1
4.4	5.7
4.5	2.7
6.2	3
0.9	1.2
0.8	4.6
0.2	4
0.9	0.6
1.3	6.8
2.6	0.4
2.6	1.2
1.2	3.7
2.7	0.3
6.3	8
4.3	11.5
1	4.2
12.2	7.6
11.9	4.3
6.5	5.3
1.2	4.3
6.1	2.4
16	1.4
0.5	4
9.8	10.7
4.3	10
5.1	2.6
3.7	1.1
17.3	9.1
0.7	5.8
2.2	11.9
1.5	0.3
1	1.3
18.6	1.8
2	3.7
1.5	2.6
3.2	1.8
4.1	1.2
16.4	3
7.2	2.3
8.2	2.1
15.2	3.2
0.1	3.6
1.2	3
7.7	9.2
2.2	6.9
9.7	12.7
4	2.5
6.5
3.5
4.7
5.8
8.7
0.4
3.2
2.5
0.4
16.6
2
9.8
12.8
4.8
2.2
5.4

Answer 1

Paired T-Test and CI: Before, After

Paired T for Before - After

N Mean StDev SE Mean
Before 12 4.583 0.900 0.260
After 12 5.167 0.835 0.241
Difference 12 -0.583 0.793 0.229

95% upper bound for mean difference: -0.172
T-Test of mean difference = 0 (vs < 0): T-Value = -2.55 P-Value = 0.014

Since~p-value<0.05, hence we reject null hypothesis and conclude that there is an evidence of improvement of ability.

Two-Sample T-Test and CI: Men, Women

Two-sample T for Men vs Women

N Mean StDev SE Mean
Men 306 5.56 5.36 0.31
Women 290 5.49 5.58 0.33

Difference = mu (Men) - mu (Women)
Estimate for difference: 0.065
95% CI for difference: (-0.816, 0.946)
T-Test of difference = 0 (vs not =): T-Value = 0.15 P-Value = 0.885 DF = 588

Since p-value>0.05, hence we fail to reject null hypothesis and there is not sufficient evidence to conclude that  men and women have different job tenures.