bus case study

Data

Employee	Starting Salary	On Road Pct Author: Percentage of time on the road with a client	State Univ Author: Whether the employee graduated from State University	CIS Degree Author: Whether the employee got his/her degree in the computer information systems area (or a similar area)	Stayed 3 Years Author: Whether the employee stayed with the company for at least 3 years	Tenure Author: Number of months employee stayed with the company (for those who left before 3 years)
1	38900	57%	Yes	Yes	No	11
2	42300	68%	Yes	Yes	No	5
3	39800	75%	No	Yes	No	21
5	40400	71%	No	Yes	No	19
6	36400	62%	No	Yes	No	18
8	36600	37%	No	Yes	No	17
9	34600	65%	No	Yes	No	20
10	42300	53%	Yes	Yes	No	16
12	39700	60%	No	Yes	No	12
17	35500	50%	No	Yes	No	15
23	37200	59%	Yes	Yes	No	14
25	36600	45%	No	Yes	No	13
26	41000	81%	Yes	Yes	No	9
27	40800	111%	Yes	Yes	No	7
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
37	39500	62%	No	Yes	No	5
38	37800	20%	No	Yes	No	23
39	38600	57%	No	Yes	No	8
43	36200	68%	No	Yes	No	31
44	39600	59%	No	Yes	No	10
47	39500	53%	Yes	Yes	No	17
51	39400	34%	Yes	Yes	No	27
56	37200	64%	Yes	Yes	No	23
60	37900	76%	Yes	Yes	No	14
61	37900	58%	No	Yes	No	26
62	37900	28%	No	Yes	No	14
64	37400	49%	No	Yes	No	19
66	36600	51%	Yes	Yes	No	7
4	35700	29%	No	Yes	Yes
7	37300	41%	Yes	No	Yes
11	37800	73%	No	Yes	Yes
13	36100	56%	Yes	Yes	Yes
14	36100	42%	Yes	Yes	Yes
15	33800	35%	No	Yes	Yes
16	38900	36%	No	Yes	Yes
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
24	37700	55%	Yes	Yes	Yes
28	36700	56%	Yes	Yes	Yes
36	36900	42%	No	Yes	Yes
40	40600	70%	Yes	Yes	Yes
41	41600	63%	Yes	Yes	Yes
42	40800	44%	No	No	Yes
45	36100	56%	Yes	Yes	Yes
46	36100	42%	No	Yes	Yes
48	39100	38%	No	Yes	Yes
49	40300	53%	Yes	Yes	Yes
50	38800	78%	Yes	Yes	Yes
52	38400	23%	No	Yes	Yes
53	35200	33%	No	Yes	Yes
54	36100	24%	No	No	Yes
55	37100	44%	No	Yes	Yes
57	36800	46%	Yes	No	Yes
58	36500	27%	No	No	Yes
59	35900	29%	No	No	Yes
63	36700	37%	No	Yes	Yes
65	38200	62%	Yes	Yes	Yes

1(b)

Starting Salary	The 95% confidence interval for the mean starting salary for those who stay atleast 3 years with D & Y can be calculated as follows:
Stayed 3 Years	Did not stay 3 years	Sample Size, n =	32
35700	38900	Mean, µ =	37381
37300	42300	Standard Deviation, σ =	1805.98
37800	39800	Level of Significance, α =	0.05	[Please click on the respective cells to view the formulas and calculations]
36100	40400	Critical Value, z(α/2) =	1.960
36100	36400
33800	36600	Lower Confidence Limit:	36755.52
38900	34600	Upper Confidence Limit:	38006.98
37600	42300
38100	39700	The 95% confidence interval for the mean starting salary for those who did not stay atleast 3 years with D & Y can be calculated as follows:
38300	35500	Sample Size, n =	34
34600	37200	Mean, µ =	38556
36300	36600	Standard Deviation, σ =	1887.15
37700	41000	Level of Significance, α =	0.05
36700	40800	Critical Value, z(α/2) =	1.960
36900	37700
40600	37700	Lower Confidence Limit:	37921.55
41600	39300	Upper Confidence Limit:	39190.21
40800	37500
36100	40000	The 95% confidence interval for the difference of the means can be calculated as follows:
36100	41500	Stayed 3 Years	Did not stay 3 years
39100	39600	Mean	37381	38555.88
40300	39500	Standard Deviation	1805.98	1887.15
38800	37800	Sample Size	32	34
38400	38600	Alpha	0.05
35200	36200
36100	39600	Mean Difference	-1174.63
37100	39500	Standard Error	454.609
36800	39400	Zα/2	1.96
36500	37200	Margin of Error	891.02
35900	37900
36700	37900	Lower Confidence Limit	-2065.65
38200	37900	Upper Confidence Limit	-283.62
37400
36600

1(c)

For all employees whose starting salary is below the median, the 95% confidence interval for the proportion of employees who stay with D & Y for atleast 3 years can be calculated as follows:
Sample Size =	33
Number of Successes =	20
Sample Proportion =	0.61	[Please click on the respective cells to view the formulas and calculations]
Level of Significance, α =	0.05
Critical Value, z(α/2) =	1.96
Lower Confidence Level	0.439
Upper Confidence Level	0.773
For all employees whose starting salary is above the median, the 95% confidence interval for the proportion of employees who stay with D & Y for atleast 3 years can be calculated as follows:
Sample Size =	33
Number of Successes =	12
Sample Proportion =	0.36
Level of Significance, α =	0.05
Critical Value, z(α/2) =	1.96
Lower Confidence Level	0.200
Upper Confidence Level	0.528
95% confidence interval for the difference between the two proportions can be calculated as follows:
Above the median	Below the median
Outcome	12	20
Sample Size	33	33
Sample Proportion	0.3636	0.6061
Alpha	0.05
Point Difference for Population Proportions	-0.242
Standard Error	0.119
Zα/2	1.960
Margin of Error	0.234
Lower Confidence Limit	-0.4764
Upper Confidence Limit	-0.0085

2

For all employees whose percentage of time on road is below the median, the 95% confidence interval for the proportion of employees who stay with D & Y for atleast 3 years can be calculated as follows:
Sample Size =	33
Number of Successes =	21
Sample Proportion =	0.64	[Please click on the respective cells to view the formulas and calculations]
Level of Significance, α =	0.05
Critical Value, z(α/2) =	1.96
Lower Confidence Level	0.472
Upper Confidence Level	0.800
For all employees whose percentage of time on road is above the median, the 95% confidence interval for the proportion of employees who stay with D & Y for atleast 3 years can be calculated as follows:
Sample Size =	33
Number of Successes =	11
Sample Proportion =	0.33
Level of Significance, α =	0.05
Critical Value, z(α/2) =	1.96
Lower Confidence Level	0.172
Upper Confidence Level	0.494
95% confidence interval for the difference between the two proportions can be calculated as follows:
Above the median	Below the median
Outcome	11	21
Sample Size	33	33
Sample Proportion	0.3333	0.6364
Alpha	0.05
Point Difference for Population Proportions	-0.303
Standard Error	0.117
Zα/2	1.960
Margin of Error	0.230
Lower Confidence Limit	-0.5328
Upper Confidence Limit	-0.0732

3

Stayed 3 Years Author: Whether the employee stayed with the company for at least 3 years	Tenure Author: Number of months employee stayed with the company (for those who left before 3 years)	The 95% confidence interval for the mean tenure for those who leave D & Y within 3 years can be calculated as follows:
No	11	Sample Size, n =	34
No	5	Mean, µ =	15
No	21	Standard Deviation, σ =	6.62
No	19	Level of Significance, α =	0.05	[Please click on the respective cells to view the formulas and calculations]
No	18	Critical Value, z(α/2) =	1.960
No	17
No	20	Lower Confidence Limit:	13.07
No	16	Upper Confidence Limit:	17.52
No	12
No	15
No	14
No	13
No	9
No	7
No	22
No	11
No	16
No	18
No	9
No	5
No	18
No	5
No	23
No	8
No	31
No	10
No	17
No	27
No	23
No	14
No	26
No	14
No	19
No	7

4

For all employees with CIS Degrees, the 95% confidence interval for the proportion of employees who stay with D & Y for atleast 3 years can be calculated as follows:
Sample Size =	58
Number of Successes =	25
Sample Proportion =	0.43	[Please click on the respective cells to view the formulas and calculations]
Level of Significance, α =	0.05
Critical Value, z(α/2) =	1.96
Lower Confidence Level	0.304
Upper Confidence Level	0.558
For all employees without CIS Degrees, the 95% confidence interval for the proportion of employees who stay with D & Y for atleast 3 years can be calculated as follows:
Sample Size =	8
Number of Successes =	7
Sample Proportion =	0.88
Level of Significance, α =	0.05
Critical Value, z(α/2) =	1.96
Lower Confidence Level	0.646
Upper Confidence Level	1.104

1

2

3

4

5

6

7

8

9

A

B

C

Stayed 3 Years

Did not stay 3 years

35700

38900

37300

42300

37800

39800

36100

40400

36100

36400

33800

36600

38900

34600

Starting Salary