Ashford 3: - Week 2 - Assignment

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Problem Set Week Two

In the Week Two Assignment sheet, complete the problems below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and Week 1 assignment sheet.

See comments at the right of the data set.
ID	Salary	Compa	Midpoint	Age	Performance Rating	Service	Gender	Raise	Degree	Gender1	Grade
8	23	1.000	23	32	90	9	1	5.8	0	F	A	The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
10	22	0.956	23	30	80	7	1	4.7	0	F	A	Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11	23	1.000	23	41	100	19	1	4.8	0	F	A
14	24	1.043	23	32	90	12	1	6	0	F	A	The column labels in the table mean:
15	24	1.043	23	32	80	8	1	4.9	0	F	A	ID – Employee sample number	Salary – Salary in thousands
23	23	1.000	23	36	65	6	1	3.3	1	F	A	Age – Age in years		Performance Rating – Appraisal rating (Employee evaluation score)
26	24	1.043	23	22	95	2	1	6.2	1	F	A	Service – Years of service (rounded)	Gender: 0 = male, 1 = female
31	24	1.043	23	29	60	4	1	3.9	0	F	A	Midpoint – salary grade midpoint	Raise – percent of last raise
35	24	1.043	23	23	90	4	1	5.3	1	F	A	Grade – job/pay grade	Degree (0= BS\BA 1 = MS)
36	23	1.000	23	27	75	3	1	4.3	1	F	A	Gender1 (Male or Female)	Compa - salary divided by midpoint
37	22	0.956	23	22	95	2	1	6.2	1	F	A
42	24	1.043	23	32	100	8	1	5.7	0	F	A
3	34	1.096	31	30	75	5	1	3.6	0	F	B
18	36	1.161	31	31	80	11	1	5.6	1	F	B
20	34	1.096	31	44	70	16	1	4.8	1	F	B
39	35	1.129	31	27	90	6	1	5.5	1	F	B
7	41	1.025	40	32	100	8	1	5.7	0	F	C
13	42	1.050	40	30	100	2	1	4.7	1	F	C
22	57	1.187	48	48	65	6	1	3.8	0	F	D
24	50	1.041	48	30	75	9	1	3.8	1	F	D
45	55	1.145	48	36	95	8	1	5.2	0	F	D
17	69	1.210	57	27	55	3	1	3	0	F	E
48	65	1.140	57	34	90	11	1	5.3	1	F	E
28	75	1.119	67	44	95	9	1	4.4	1	F	F
43	77	1.149	67	42	95	20	1	5.5	1	F	F
19	24	1.043	23	32	85	1	0	4.6	1	M	A
25	24	1.043	23	41	70	4	0	4	0	M	A
40	25	1.086	23	24	90	2	0	6.3	0	M	A
2	27	0.870	31	52	80	7	0	3.9	0	M	B
32	28	0.903	31	25	95	4	0	5.6	0	M	B
34	28	0.903	31	26	80	2	0	4.9	1	M	B
16	47	1.175	40	44	90	4	0	5.7	0	M	C
27	40	1.000	40	35	80	7	0	3.9	1	M	C
41	43	1.075	40	25	80	5	0	4.3	0	M	C
5	47	0.979	48	36	90	16	0	5.7	1	M	D
30	49	1.020	48	45	90	18	0	4.3	0	M	D
1	58	1.017	57	34	85	8	0	5.7	0	M	E
4	66	1.157	57	42	100	16	0	5.5	1	M	E
12	60	1.052	57	52	95	22	0	4.5	0	M	E
33	64	1.122	57	35	90	9	0	5.5	1	M	E
38	56	0.982	57	45	95	11	0	4.5	0	M	E
44	60	1.052	57	45	90	16	0	5.2	1	M	E
46	65	1.140	57	39	75	20	0	3.9	1	M	E
47	62	1.087	57	37	95	5	0	5.5	1	M	E
49	60	1.052	57	41	95	21	0	6.6	0	M	E
50	66	1.157	57	38	80	12	0	4.6	0	M	E
6	76	1.134	67	36	70	12	0	4.5	1	M	F
9	77	1.149	67	49	100	10	0	4	1	M	F
21	76	1.134	67	43	95	13	0	6.3	1	M	F
29	72	1.074	67	52	95	5	0	5.4	0	M	F

Score:	Week 2	Testing means - T-tests
		In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing.
		In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis.

<1 point>	1	Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.
		(Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value -- see column S)
		Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female average salaries?
		Males				Females
		Ho: Mean salary = 45			Ho: Mean salary = 45
		Ha: Mean salary =/= 45			Ha: Mean salary =/= 45

		Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances,
		having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome - we are tricking Excel into doing a one sample test for us.
			Male	Ho			Female	Ho
		Mean	52	45		Mean	38	45
		Variance	316	0		Variance	334.667	0
		Observations	25	25		Observations	25	25
		Hypothesized Mean Difference	0			Hypothesized Mean Difference	0
		df	24			df	24
		t Stat	1.96890383			t Stat	-1.9132
		P(T<=t) one-tail	0.03030785			P(T<=t) one-tail	0.03386
		t Critical one-tail	1.71088208			t Critical one-tail	1.71088
		P(T<=t) two-tail	0.0606157			P(T<=t) two-tail	0.06772
		t Critical two-tail	2.06389856			t Critical two-tail	2.0639
		Conclusion: Do not reject Ho; mean equals 45	Conclusion: Do not reject Ho; mean equals 45
		Is this a 1 or 2 tail test?				Is this a 1 or 2 tail test?
		- why?				- why?
		P-value is:				P-value is:
		Is P-value > 0.05?				Is P-value > 0.05?
		Why do we not reject Ho?				Why do we not reject Ho?
	Interpretation:




<1 point>	2	Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other.
		(Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.)

		Ho:
		Ha:
		Test to use:
		Place B43 in Outcome range box.















		P-value is:
		Is P-value < 0.05?
		Reject or do not reject Ho:
	If the null hypothesis was rejected, what is the effect size value:
		Meaning of effect size measure:

		Interpretation:

	b.	Since the one and two sample t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?


<1 point>	3	Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)

		Ho:
		Ha:
		Statistical test to use:
		Place B75 in Outcome range box.















		What is the p-value:
		Is P-value < 0.05?
		Reject or do not reject Ho:
	If the null hypothesis was rejected, what is the effect size value:
		Meaning of effect size measure:

		Interpretation:

<1 point>	4	Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?

		Ho:
		Ha:

		Test to use:

		Place B106 in Outcome range box.
















			What is the p-value:
			Is P-value < 0.05?
			Do we REJ or Not reject the null?
		If the null hypothesis was rejected, what is the effect size value:
			Meaning of effect size measure:

			Interpretation:



<2 points>	5	If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality,
		which would be more appropriate to use in answering the question about salary equity? Why?
		What are your conclusions about equal pay at this point?

(Note: Questions 1- 4 have additional elements to respond to below the analysis results and included in the Week Two Assignment sheet are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.)