bus308 mangerial statistics

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week_2_bus308_data.2016.01.04.xls
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Score: Week 2 Testing means - T-tests Q3
In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. Ho Female Male Female
In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. 45 34 1.017 1.096
45 41 0.870 1.025
<1 point> 1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. 45 23 1.157 1.000
(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) 45 22 0.979 0.956
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? 45 23 1.134 1.000
Males Females 45 42 1.149 1.050
Ho: Mean salary = 45 Ho: Mean salary = 45 45 24 1.052 1.043
Ha: Mean salary =/= 45 Ha: Mean salary =/= 45 45 24 1.175 1.043
45 69 1.043 1.210
Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, 45 36 1.134 1.161
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. 45 34 1.043 1.096
Male Ho Female Ho 45 57 1.000 1.187
Mean 52 45 Mean 38 45 45 23 1.074 1.000
Variance 316 0 Variance 334.6666666667 0 45 50 1.020 1.041
Observations 25 25 Observations 25 25 45 24 0.903 1.043
Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 45 75 1.122 1.119
df 24 df 24 45 24 0.903 1.043
t Stat 1.9689038266 t Stat -1.9132063573 45 24 0.982 1.043
P(T<=t) one-tail 0.0303078503 P(T<=t) one-tail 0.0338621184 45 23 1.086 1.000
t Critical one-tail 1.7108820799 t Critical one-tail 1.7108820799 45 22 1.075 0.956
P(T<=t) two-tail 0.0606157006 P(T<=t) two-tail 0.0677242369 45 35 1.052 1.129
t Critical two-tail 2.0638985616 t Critical two-tail 2.0638985616 45 24 1.140 1.043
Conclusion: Do not reject Ho; mean equals 45 Conclusion: Do not reject Ho; mean equals 45 45 77 1.087 1.149
Is this a 1 or 2 tail test? Is this a 1 or 2 tail test?
- why? - why?
P-value is: P-value is: 45 55 1.052 1.145
Is P-value > 0.05? Is P-value > 0.05? 45 65 1.157 1.140
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?

Data

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr
1 64.4 1.130 57 34 85 8 0 5.7 0 M E 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)?
2 27.4 0.884 31 52 80 7 0 3.9 0 M B Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3 35.6 1.148 31 30 75 5 1 3.6 1 F B
4 62.3 1.093 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 48.7 1.014 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 75 1.120 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score)
7 41.8 1.046 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 23.7 1.029 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 76.8 1.147 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 24 1.044 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa - salary divided by midpoint
11 23.9 1.041 23 41 100 19 1 4.8 1 F A
12 62.5 1.096 57 52 95 22 0 4.5 0 M E
13 42.7 1.067 40 30 100 2 1 4.7 0 F C
14 23.4 1.016 23 32 90 12 1 6 1 F A
15 23.3 1.012 23 32 80 8 1 4.9 1 F A
16 48.7 1.217 40 44 90 4 0 5.7 0 M C
17 65.1 1.142 57 27 55 3 1 3 1 F E
18 34.6 1.116 31 31 80 11 1 5.6 0 F B
19 24.5 1.065 23 32 85 1 0 4.6 1 M A
20 34.9 1.125 31 44 70 16 1 4.8 0 F B
21 76.5 1.142 67 43 95 13 0 6.3 1 M F
22 57.8 1.204 48 48 65 6 1 3.8 1 F D
23 22.7 0.987 23 36 65 6 1 3.3 0 F A
24 56.5 1.177 48 30 75 9 1 3.8 0 F D
25 24.5 1.064 23 41 70 4 0 4 0 M A
26 23.2 1.010 23 22 95 2 1 6.2 0 F A
27 46.8 1.171 40 35 80 7 0 3.9 1 M C
28 76.6 1.144 67 44 95 9 1 4.4 0 F F
29 75.9 1.133 67 52 95 5 0 5.4 0 M F
30 47.4 0.987 48 45 90 18 0 4.3 0 M D
31 25.3 1.101 23 29 60 4 1 3.9 1 F A
32 27.2 0.878 31 25 95 4 0 5.6 0 M B
33 66 1.158 57 35 90 9 0 5.5 1 M E
34 28.1 0.907 31 26 80 2 0 4.9 1 M B
35 22.5 0.980 23 23 90 4 1 5.3 0 F A
36 22.7 0.985 23 27 75 3 1 4.3 0 F A
37 23.4 1.017 23 22 95 2 1 6.2 0 F A
38 58.5 1.026 57 45 95 11 0 4.5 0 M E
39 35.5 1.144 31 27 90 6 1 5.5 0 F B
40 24.8 1.078 23 24 90 2 0 6.3 0 M A
41 45.8 1.144 40 25 80 5 0 4.3 0 M C
42 22.2 0.965 23 32 100 8 1 5.7 1 F A
43 77.4 1.155 67 42 95 20 1 5.5 0 F F
44 58.8 1.032 57 45 90 16 0 5.2 1 M E
45 51.2 1.066 48 36 95 8 1 5.2 1 F D
46 61.3 1.076 57 39 75 20 0 3.9 1 M E
47 64.3 1.128 57 37 95 5 0 5.5 1 M E
48 67.6 1.186 57 34 90 11 1 5.3 1 F E
49 61.3 1.075 57 41 95 21 0 6.6 0 M E
50 66.1 1.159 57 38 80 12 0 4.6 0 M E

Sheet1

Sal Compa G Mid Age EES SR G Raise Deg SUMMARY OUTPUT SUMMARY OUTPUT
24 1.045 1 23 32 90 9 1 5.8 1
24.2 1.053 1 23 30 80 7 1 4.7 1 Regression Statistics Regression Statistics
23.4 1.018 1 23 41 100 19 1 4.8 1 Multiple R 0.7050179484 Multiple R 0.9931286935
23.4 1.017 1 23 32 90 12 1 6 1 R Square 0.4970503076 R Square 0.9863046018
22.6 0.983 1 23 32 80 8 1 4.9 1 Adjusted R Square 0.4132253589 Adjusted R Square 0.9840220355
22.9 0.995 1 23 36 65 6 1 3.3 0 Standard Error 0.0561252686 Standard Error 2.4352822665
23.1 1.003 1 23 22 95 2 1 6.2 0 Observations 50 Observations 50
23.3 1.011 1 23 29 60 4 1 3.9 1
22.7 0.985 1 23 23 90 4 1 5.3 0 ANOVA ANOVA
23.5 1.023 1 23 27 75 3 1 4.3 0 df SS MS F Significance F df SS MS F Significance F
23 1.002 1 23 22 95 2 1 6.2 0 Regression 7 0.1307500775 0.0186785825 5.9296225662 0.0000782906 Regression 7 17938.424611863 2562.632087409 432.1033638177 5.29906273684337E-37
24 1.042 1 23 32 100 8 1 5.7 1 Residual 42 0.1323019225 0.0031500458 Residual 42 249.085188137 5.9305997175
35.5 1.145 1 31 30 75 5 1 3.6 1 Total 49 0.263052 Total 49 18187.5098
34.7 1.119 1 31 31 80 11 1 5.6 0
35.5 1.146 1 31 44 70 16 1 4.8 0 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
35.2 1.136 1 31 27 90 6 1 5.5 0 Intercept 0.9486238772 0.0817167716 11.6086803119 0 0.7837127557 1.1135349987 0.7837127557 1.1135349987 Intercept -4.8714544587 3.54570071 -1.3739045839 0.1767599037 -12.0269681853 2.2840592678 -12.0269681853 2.2840592678
40.4 1.01 1 40 32 100 8 1 5.7 1 Mid 0.0034995027 0.0006492568 5.3900133356 0.0000029767 0.0021892495 0.0048097559 0.0021892495 0.0048097559 Mid 1.2284155048 0.0281713308 43.6051641629 1.32019333894083E-36 1.1715634576 1.2852675521 1.1715634576 1.2852675521
42.7 1.068 1 40 30 100 2 1 4.7 0 Age 0.0005527738 0.0014459446 0.3822925256 0.7041721007 -0.0023652605 0.0034708081 -0.0023652605 0.0034708081 Age 0.0368279425 0.0627397124 0.5869957178 0.5603489282 -0.0897859231 0.1634418081 -0.0897859231 0.1634418081
53.4 1.112 1 48 48 65 6 1 3.8 1 EES -0.0018462553 0.0010252155 -1.8008461371 0.0789105539 -0.0039152239 0.0002227133 -0.0039152239 0.0002227133 EES -0.0821579785 0.0444842245 -1.8469014451 0.0718147225 -0.171930778 0.007614821 -0.171930778 0.007614821
51.5 1.072 1 48 30 75 9 1 3.8 0 SR -0.0004182288 0.0018278101 -0.2288141345 0.820123898 -0.004106899 0.0032704414 -0.004106899 0.0032704414 SR -0.0778484529 0.079308905 -0.9815852701 0.3319249969 -0.2379003029 0.0822033971 -0.2379003029 0.0822033971
49.8 1.037 1 48 36 95 8 1 5.2 1 G 0.0646649961 0.0183396697 3.5259629624 0.001034866 0.0276540443 0.101675948 0.0276540443 0.101675948 G 2.9145083112 0.7957605113 3.6625445343 0.000693549 1.3085985836 4.5204180389 1.3085985836 4.5204180389
68.3 1.198 1 57 27 55 3 1 3 1 Raise 0.0146549564 0.0139088976 1.0536389608 0.2980722322 -0.0134143354 0.0427242483 -0.0134143354 0.0427242483 Raise 0.6763294824 0.6035087689 1.1206622295 0.2687988764 -0.5416005215 1.8942594864 -0.5416005215 1.8942594864
65.4 1.148 1 57 34 90 11 1 5.3 1 Deg 0.0014675988 0.0161098249 0.0910996125 0.9278465471 -0.0310433441 0.0339785418 -0.0310433441 0.0339785418 Deg 0.0345044482 0.6990072742 0.0493620731 0.9608647532 -1.3761493419 1.4451582383 -1.3761493419 1.4451582383
78.4 1.17 1 67 44 95 9 1 4.4 0
75.9 1.133 1 67 42 95 20 1 5.5 0
24 1.044 0 23 32 85 1 0 4.6 1
23.3 1.012 0 23 41 70 4 0 4 0
24.1 1.049 0 23 24 90 2 0 6.3 0
27.5 0.887 0 31 52 80 7 0 3.9 0 t-Test: Two-Sample Assuming Equal Variances
27.1 0.875 0 31 25 95 4 0 5.6 0
27.7 0.895 0 31 26 80 2 0 4.9 1 Variable 1 Variable 2
40.8 1.019 0 40 44 90 4 0 5.7 0 Mean 1.06684 1.04836
43.9 1.097 0 40 35 80 7 0 3.9 1 Variance 0.00430164 0.00648099
41 1.025 0 40 25 80 5 0 4.3 0 Observations 25 25
48.7 1.014 0 48 36 90 16 0 5.7 1 Pooled Variance 0.005391315
49.4 1.029 0 48 45 90 18 0 4.3 0 Hypothesized Mean Difference 0
64.4 1.13 0 57 34 85 8 0 5.7 0 df 48
64.5 1.132 0 57 42 100 16 0 5.5 1 t Stat 0.8898352784
58.9 1.033 0 57 52 95 22 0 4.5 0 P(T<=t) one-tail 0.188996287
57.9 1.016 0 57 35 90 9 0 5.5 1 t Critical one-tail 1.6772241961
59 1.035 0 57 45 95 11 0 4.5 0 P(T<=t) two-tail 0.3779925741
63.3 1.111 0 57 45 90 16 0 5.2 1 t Critical two-tail 2.0106347576
56.8 0.996 0 57 39 75 20 0 3.9 1
58 1.017 0 57 37 95 5 0 5.5 1
62.4 1.094 0 57 41 95 21 0 6.6 0
63.8 1.12 0 57 38 80 12 0 4.6 0
79 1.179 0 67 36 70 12 0 4.5 1
77 1.149 0 67 49 100 10 0 4 1
74.8 1.116 0 67 43 95 13 0 6.3 1
76 1.135 0 67 52 95 5 0 5.4 0