BUS 308 - Statistics Wk 4 Problem set

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equal_pay___student_rev_4_3.xlsx
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Data

ID Sal Compa Mid Age EES SER G Raise Deg Gen1 Gr
1 58 1.017 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 0.870 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 34 1.096 31 30 75 5 1 3.6 1 F B
4 66 1.157 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 47 0.979 48 36 90 16 0 5.7 1 M D ID – Employee sample number Sal – Salary in thousands
6 76 1.134 67 36 70 12 0 4.5 1 M F Age – Age in years EES – Appraisal rating (Employee evaluation score)
7 41 1.025 40 32 100 8 1 5.7 1 F C SER – Years of service G – Gender (0 = male, 1 = female)
8 23 1.000 23 32 90 9 1 5.8 1 F A Mid – salary grade midpoint Raise – percent of last raise
9 77 1.149 67 49 100 10 0 4 1 M F Grade – job/pay grade Deg (0= BS\BA 1 = MS)
10 22 0.956 23 30 80 7 1 4.7 1 F A Gen1 (Male or Female) Compa - salary divided by midpoint, a measure of salary that removes the impact of grade
11 23 1.000 23 41 100 19 1 4.8 1 F A
12 60 1.052 57 52 95 22 0 4.5 0 M E This data should be treated as a sample of employees taken from a company that has about 1,000
13 42 1.050 40 30 100 2 1 4.7 0 F C employees using a random sampling approach.
14 24 1.043 23 32 90 12 1 6 1 F A
15 24 1.043 23 32 80 8 1 4.9 1 F A
16 47 1.175 40 44 90 4 0 5.7 0 M C Mac Users: The homework in this course assumes students have Windows Excel, and
17 69 1.210 57 27 55 3 1 3 1 F E can load the Analysis ToolPak into their version of Excel.
18 36 1.161 31 31 80 11 1 5.6 0 F B The analysis tool pak has been removed from Excel for Windows, but a free third-party
19 24 1.043 23 32 85 1 0 4.6 1 M A tool that can be used (found on an answers Microsoft site) is:
20 34 1.096 31 44 70 16 1 4.8 0 F B http://www.analystsoft.com/en/products/statplusmacle
21 76 1.134 67 43 95 13 0 6.3 1 M F Like the Microsoft site, I make cannot guarantee the program, but do know that
22 57 1.187 48 48 65 6 1 3.8 1 F D Statplus is a respected statistical package. You may use other approaches or tools
23 23 1.000 23 36 65 6 1 3.3 0 F A as desired to complete the assignments.
24 50 1.041 48 30 75 9 1 3.8 0 F D
25 24 1.043 23 41 70 4 0 4 0 M A
26 24 1.043 23 22 95 2 1 6.2 0 F A
27 40 1.000 40 35 80 7 0 3.9 1 M C
28 75 1.119 67 44 95 9 1 4.4 0 F F
29 72 1.074 67 52 95 5 0 5.4 0 M F
30 49 1.020 48 45 90 18 0 4.3 0 M D
31 24 1.043 23 29 60 4 1 3.9 1 F A
32 28 0.903 31 25 95 4 0 5.6 0 M B
33 64 1.122 57 35 90 9 0 5.5 1 M E
34 28 0.903 31 26 80 2 0 4.9 1 M B
35 24 1.043 23 23 90 4 1 5.3 0 F A
36 23 1.000 23 27 75 3 1 4.3 0 F A
37 22 0.956 23 22 95 2 1 6.2 0 F A
38 56 0.982 57 45 95 11 0 4.5 0 M E
39 35 1.129 31 27 90 6 1 5.5 0 F B
40 25 1.086 23 24 90 2 0 6.3 0 M A
41 43 1.075 40 25 80 5 0 4.3 0 M C
42 24 1.043 23 32 100 8 1 5.7 1 F A
43 77 1.149 67 42 95 20 1 5.5 0 F F
44 60 1.052 57 45 90 16 0 5.2 1 M E
45 55 1.145 48 36 95 8 1 5.2 1 F D
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
48 65 1.140 57 34 90 11 1 5.3 1 F 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
http://www.analystsoft.com/en/products/statplusmacle

Week 4

Week 4 Confidence Intervals and Chi Square (Chs 11 - 12) Let's look at some other factors that might influence pay. Q1 Q2 <Note: use right click on row numbers to insert rows to perform analysis below any question>
For question 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. Gr Deg Gen1 Sal
For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. A 0 F 34
1 One question we might have is if the distribution of graduate and undergraduate degrees independent of the grade the employee? A 0 F 41
(Note: this is the same as asking if the degrees are distributed the same way.)
Based on the analysis of our sample data (shown below), what is your answer?
Ho: The populaton correlation between grade and degree is 0. C 0 F 77
Ha: The population correlation between grade and degree is > 0
Perform analysis:
OBSERVED A B C D E F Total
COUNT - M or 0 7 5 3 2 5 3 25
COUNT - F or 1 8 2 2 3 7 3 25
total 15 7 5 5 12 6 50
EXPECTED
7.5 3.5 2.5 2.5 6 3 25 <Highlighting each cell with show how the value
7.5 3.5 2.5 2.5 6 3 25 is found: row total times column total divided by
15 7 5 5 12 6 50 grand total.>
By using either the Excel Chi Square functions or calculating the results directly as the text shows, do we
reject or not reject the null hypothesis? What does your conclusion mean?
Interpretation:
2 Using our sample data, we can construct a 95% confidence interval for the population's mean salary for each gender.
Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?
Males Mean St error Low to High
52 3.6587793957 44.4482793272 59.5517206728 Results are mean +/-2.064*standard error
Females 38 3.6227541769 30.5226353789 45.4773646211 2.064 is t value for 95% interval
<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>
Interpretation:
C 0 F 55
D 1 M 77
3 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? D 1 M 60
4 Using our sample data, construct a 95% confidence interval for the population's mean service difference for each gender.
Do they intersect or overlap? How do these results compare to the findings in week 2, question 2?
5 How do you interpret these results in light of our question about equal pay for equal work?