Question

1. What is the 95% CI for the difference between the mean starting salaries of those who stay at least three years and those who leave before 3 years?  Can you say that you are 95% sure there is a difference?

Case Study: Employee Retention at D&Y
Employee	Starting Salary	On Road Pct	State Univ	CIS Degree	Stayed 3 Years	Tenure
1	38900	57%	Yes	Yes	No	11
2	42300	68%	Yes	Yes	No	5
3	39800	75%	No	Yes	No	21
4	35700	29%	No	Yes	Yes
5	40400	71%	No	Yes	No	19
6	36400	62%	No	Yes	No	18
7	37300	41%	Yes	No	Yes
8	36600	37%	No	Yes	No	17
9	34600	65%	No	Yes	No	20
10	42300	53%	Yes	Yes	No	16
11	37800	73%	No	Yes	Yes
12	39700	60%	No	Yes	No	12
13	36100	56%	Yes	Yes	Yes
14	36100	42%	Yes	Yes	Yes
15	33800	35%	No	Yes	Yes
16	38900	36%	No	Yes	Yes
17	35500	50%	No	Yes	No	15
18	37600	58%	No	Yes	Yes
19	38100	78%	Yes	Yes	Yes
20	38300	16%	No	No	Yes
21	34600	29%	No	Yes	Yes
22	36300	26%	No	Yes	Yes
23	37200	59%	Yes	Yes	No	14
24	37700	55%	Yes	Yes	Yes
25	36600	45%	No	Yes	No	13
26	41000	81%	Yes	Yes	No	9
27	40800	111%	Yes	Yes	No	7
28	36700	56%	Yes	Yes	Yes
29	37700	56%	No	Yes	No	22
30	37700	42%	No	Yes	No	11
31	39300	69%	Yes	Yes	No	16
32	37500	50%	No	Yes	No	18
33	40000	69%	Yes	Yes	No	9
34	41500	64%	Yes	No	No	5
35	39600	72%	No	Yes	No	18
36	36900	42%	No	Yes	Yes
37	39500	62%	No	Yes	No	5
38	37800	20%	No	Yes	No	23
39	38600	57%	No	Yes	No	8
40	40600	70%	Yes	Yes	Yes
41	41600	63%	Yes	Yes	Yes
42	40800	44%	No	No	Yes
43	36200	68%	No	Yes	No	31
44	39600	59%	No	Yes	No	10
45	36100	56%	Yes	Yes	Yes
46	36100	42%	No	Yes	Yes
47	39500	53%	Yes	Yes	No	17
48	39100	38%	No	Yes	Yes
49	40300	53%	Yes	Yes	Yes
50	38800	78%	Yes	Yes	Yes
51	39400	34%	Yes	Yes	No	27
52	38400	23%	No	Yes	Yes
53	35200	33%	No	Yes	Yes
54	36100	24%	No	No	Yes
55	37100	44%	No	Yes	Yes
56	37200	64%	Yes	Yes	No	23
57	36800	46%	Yes	No	Yes
58	36500	27%	No	No	Yes
59	35900	29%	No	No	Yes
60	37900	76%	Yes	Yes	No	14
61	37900	58%	No	Yes	No	26
62	37900	28%	No	Yes	No	14
63	36700	37%	No	Yes	Yes
64	37400	49%	No	Yes	No	19
65	38200	62%	Yes	Yes	Yes
66	36600	51%	Yes	Yes	No	7

Answer 1

We use minitab to solve this question-

We first test is the variance equal for salaries of Leave before 3 years and Stay at least three years.

Ho : S1² = S2²            Vs   Ha : S1² S2²

The test statistics is,

F = S1² / S2^{2   ,}    S1² - Larger sample variance betwwen Leave before 3 years and

                           Stay at least three years and

                           S2² - smaller sample variance between Leave before 3 years

                                 and Stay at least three years .

= 3600471 / 2968129

F =1.213044

P-value = P( F < 1.213044) = 0.2926

P-value > 0.05 , Do not reject Ho

Therefore we use pooled variance.

We use t test with pooled standard deviation as the variances of the salaries of Leave before 3 years and Stay at least three years are equal.

Minitab output-

MTB > TwoSample 'Leave before 3 years' 'Stay at least three years';
SUBC>   Confidence 95.0;
SUBC>   Test 0.0;
SUBC>   Alternative 0;
SUBC>   Pooled.

Two-Sample T-Test and CI: Leave before 3 years, Stay at least three years

Two-sample T for Leave before 3 years vs Stay at least three years

                           N   Mean StDev SE Mean
Leave before 3 years      35 38620   1897      321
Stay at least three year 31 37271   1723      309

Difference = μ (Leave before 3 years) - μ (Stay at least three years)
Estimate for difference: 1349
95% CI for difference: (453, 2245)
T-Test of difference = 0 (vs ≠): T-Value = 3.01 P-Value = 0.004 DF = 64
Both use Pooled StDev = 1817.7075

___________________________________________________________________________

95% CI for the difference between the mean starting salaries of those who stay at least three years and those who leave before 3 years is (453, 2245).

From given sample information there is 95 % chance that difference lies in (453, 2245).