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 theEmployee Salary Data Set. Included in the Week Two tab of the Employee Salary Data Set
are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.
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- Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries?
- Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other.
- Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)
- What other information would you like to know to answer the question about salary equity between the genders? Why?
- If the salary and compa mean tests in questions 3 and 4 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?
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ID |
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| Sal |
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| C |
ompa
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| A |
ge
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| E |
ES
SER |
| G |
| Raise |
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| Deg |
Gen
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| Gr |
1
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| 5 |
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| 8 |
1.
Save Time On Research and Writing
Hire a Pro to Write You a 100% Plagiarism-Free Paper.
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1
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| 4 |
| 85 |
8 0
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| 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
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| 27 |
0.8
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7 0
3.
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0 M
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| B |
Note:
| to |
simplfy the analysis, we will assume that jobs within each grade comprise equal work.
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| 34 |
1.09
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31
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5 1
3.6 |
1
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| F |
B
4
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1.
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7
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0
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0
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| 5.5 |
1 M E
The column labels in the table mean: |
5
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| 47 |
0.979 |
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| 48 |
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| 36 |
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| 90 |
16 0 5.7 1 M D
ID – Employee sample number |
Sal – Salary in thousands |
6
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| 76 |
1.
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| 13 |
4
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| 67 |
36 70
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0
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| 4.5 |
1 M F
| Age |
– Age in years
| EES |
– Appraisal rating (Employee evaluation score)
7
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| 41 |
1.0
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| 100 |
8 1 5.7 1 F C
SER – Years of service |
G –
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| Gender |
(0 = male, 1 = female)
8
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| 23 |
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| 1.000 |
23 32 90 9 1
5.8 |
1 F A
| Mid |
– salary grade midpoint
Raise – percent of last raise |
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| 77 |
1.1
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| 49 |
67 49 100 10 0 4 1 M F
|
| Grade |
– job/pay grade
Deg (0= BS\BA 1 =
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| MS |
)
10
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| 22 |
0.
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| 95 |
6
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 |
|
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| 11 |
23 1.000 23 41 100
| 19 |
1
| 4.8 |
1 F A
12
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| 60 |
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| 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
1.0
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| 50 |
40 30 100 2 1 4.7 0 F C
employees using a random sampling approach. |
14 |
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| 24 |
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| 1.0
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| 43 |
23 32 90 12 1 6 1 F A
15 24
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| 1.043 |
23 32 80 8 1
| 4.9 |
1 F A
16 47
1.
| 17 |
5
40
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| 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.
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| 21 |
0
57 27
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| 55 |
3 1 3 1 F E
can load the Analysis ToolPak into their version of Excel. |
| 18 |
36
1.1
| 61 |
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
1.0
| 96 |
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
1.1
| 87 |
48 48
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| 65 |
6 1
| 3.8 |
1 F D
Statplus is a respected statistical packag
| e. |
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
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| 35 |
80 7 0
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| 3.9 |
1 M C
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| 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
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| 45 |
90 18 0
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| 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
0.9
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| 56 |
23 22 95 2 1 6.2 0 F A
|
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| 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 1
Week 1. |
Describing the dat
| a. |
|
1
Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set. |
a. For which variables in the data set does this function not work correctly for? Why? |
2
Sort the data by Gen or Gen 1 (into males and females) and find the mean and standard deviation for each gender for the following variables: |
sal, compa, age, sr and raise. |
Use either the descriptive stats function or the Fx functions (average and stdev). |
3
What is the probability for a: |
a. Randomly selected person being a male in grade E? |
| b. |
Randomly selected male being in grade E?
| c. |
Why are the results different?
4
Find: |
a.
The z score for each male salary, based on only the male salaries. |
b.
The z score for each female salary, based on only the female salaries. |
c.
The z score for each female compa, based on only the female compa values. |
d. |
The z score for each male compa, based on only the male compa values. |
e.
What do the distributions and spread suggest about male and female salaries? |
Why might we want to use compa to measure salaries between males and females? |
5
Based on this sample, what conclusions can you make about the issue of male and female pay equality? |
Are all of the results consistent with your conclusion? If not, why not? |
Week 2 |
Week 2
Testing means with the t-test |
|
| |
For questions 2 and 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. |
|
|
| For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed. |
1
Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. |
Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries? |
| Males |
| Females |
|
|
| Ho |
:
|
| Mean |
salary = 45
Ho: Mean salary = 45
| Ha: Mean salary =/= 45 |
Ha: Mean salary =/= 45
Note when performing a one sample test with
|
| ANOVA |
, the second variable (Ho) is listed as the same value for every corresponding value in the data set.
| t-Test: Two-
| Sample |
Assuming Unequal
|
|
|
| Variance |
s
t-Test: Two-Sample Assuming Unequal Variances
Since the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situation |
Male Ho Female Ho
Mean 52 45 Mean 38 45
Variance
316 |
0 Variance
334.6666666667 |
0
|
| Observations |
25 25 Observations 25 25
| Hypothesized Mean Difference |
0 Hypothesized Mean Difference 0
|
|
| df |
24 df 24
|
| t Stat |
1.9689038266 |
t Stat
-1.9132063573 |
| P(T<=t) one-tail |
| 0.030 |
3078503
P(T<=t) one-tail
0.0338621184 |
| t Critical one-tail |
| 1.7108820799 |
t Critical one-tail 1.7108820799
| P(T<=t) two-tail |
0.0606157006 |
P(T<=t) two-tail
| 0.067 |
7242369
| t Critical two-tail |
| 2.0638985616 |
t Critical two-tail 2.0638985616
| Conclusion: Do not reject Ho; mean equals 45 |
Conclusion: Do not reject Ho; mean equals 45
|
|
|
| Interpretation: |
2
Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other. |
3
Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.) |
4
What other information would you like to know to answer the question about salary equity between the genders? Why? |
5
If the salary and compa mean tests in questions 3 and 4 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? |
Week 3 |
Week 3
Testing multiple means with ANOVA |
For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. |
For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed.
1. |
Based on the sample data, can the average(mean) salary in the population be the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.) |
Set up the input table/range to use as follows: Put all of the salary values for each grade under the appropriate grade label. |
Be sure to incllude the null and alternate hypothesis along with the statistical test and result. |
A B C D E F
Note: Assume equal variances for all grades. |
2. |
The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results. |
Grade
Gender A B C D E F
M 24 27 40 47 56 76
The salary values were randomly picked for each cell. |
25 28 47 49 66 77
F 22 34 41 50 65 75
24 36 42 57 69 77
Ho:
|
|
| Average |
salaries are equal for all grades
Ha: Average salaries are not equal for all grades |
Ho: Average salaries by gender are equal |
Ha: Average salaries by gender are not equal |
Ho:
| Interaction |
is not significant
Ha: Interaction is significant |
| Perform analysis: |
Anova: Two-Factor With Replication |
SUMMARY |
A B C D E F
|
|
|
| Total |
M
|
| Count |
2 2 2 2 2 2 12
|
| Sum |
49 55 87 96 122
153 |
562 |
Average
|
| 24.5 |
2
|
| 7.5 |
4
|
| 3.5 |
48 61
76.5 |
46.
| 83 |
33333333
Variance
|
|
| 0.5 |
0.5 24.5 2 50 0.5
364.5151515
| 152 |
F
Count 2 2 2 2 2 2 12
Sum 46 70 83
107 |
134 152
592 |
Average 23 35
41.5 |
53.5 |
67 76
49.3333333333 |
Variance 2 2 0.5 24.5 8 2
367.3333333333 |
Total
Count 4 4 4 4 4 4
Sum 95
125 |
170 |
203 |
256 |
305 |
Average
23.75 |
31.25 |
4
|
|
|
| 2.5 |
50.75 |
64
76.25 |
Variance
1.5833333333 |
19.5833333333 |
9.6666666667 |
18.9166666667 |
31.3333333333 |
0.9166666667 |
ANOVA
Source of Variation |
| SS |
df MS F
| P-value |
F crit |
Sample
| 37.5 |
1 37.5
3.8461538462 |
0.0734833371 |
4.7472253467 |
Columns |
7841.8333333333 |
5
1568.3666666667 |
160.8581196581 |
| 0.000 |
0000001
| 3.1058752391 |
Note: a number with an E after it (E9 or E-6, for example) |
Interaction
91.5 |
5
18.3 |
1.8769230769 |
0.1723082608 |
3.1058752391
means we move the decimal point that number of places. |
Within |
117 |
12
9.75 |
For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456 |
Total
8087.8333333333 |
23
Do we reject or not reject each of the null hypotheses? What do your conclusions mean about the population values being tested? |
Interpretation:
3. |
Using our sample results, can we say that the compa values in the population are equal by grade and/or gender, and are independent of each factor? |
Grade
| Be sure to include the null and alternate hypothesis along with the statistical test and result. |
Gender A B C D E F
|
M
for the intersection of M and A might be 1.043.> |
|
F
salary values used in question 2 for a more direct comparison of the two |
outcomes.> |
Conduct and show the results of a 2-way ANOVA with replication using the completed table above. The results should look something like those in question 2. |
Interpret the results. Are the average compas for each gender (listed as sample) equal? For each grade? Do grade and gender interaction impact compa values? |
4. |
Pick any other variable you are interested in and do a simple 2-way ANOVA without replication. Why did you pick this variable and what do the results show? |
Variable name: |
Be sure to include the null and alternate hypothesis along with the statistical test and result.
Gender A B C D E F
M
Hint: use mean values in the boxes. |
F
5. |
Using the results for this week, What are your conclusions about gender equal pay for equal work at this point? |
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 |
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
<
| High |
lighting 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 |
|
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 salary 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? |
Week 5
Week 5 Correlation and
| Regression |
For each question involving a statistical test below, list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. |
For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed.
1
Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.) |
a. Interpret the results. What variables seem to be important in seeing if we pay males and females equally for equal work? |
2
Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Mid, |
age, ees, sr, raise, and deg variables.) (Note: since salary and compa are different ways of |
expressing an employee’s salary, we do not want to have both used in the same regression.) |
Ho: The regression equation is not significant. |
Ha: The regression equation is significant. |
Ho: The regression coefficient for each variable is not significant |
Ha: The regression coefficient for each variable is significant |
Sal
The analysis used Sal as the y (dependent variable) and |
SUMMARY OUTPUT |
mid, age, ees, sr, g, raise, and deg as the dependent |
variables (entered as a range). |
Regression Statistics |
Multiple R |
0.9921549762 |
R Square |
0.9843714969 |
Adjusted R Square |
0.9817667464 |
| Standard Error |
2.5927763074 |
Observations 50
ANOVA
df SS MS F
Significance F |
Regression 7
17783.6554628284 |
2540.5222089755 |
377.9139268848 |
8.44042689148567E-36 |
Residual |
42
282.3445371716 |
6.7224889803 |
Total 49
18066 |
Coefficients |
Standard Error t Stat P-value
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
Intercept |
-4.009 |
3.775 |
-1.062 |
0.294 |
| -11.627 |
| 3.609 |
-11.627 3.609
Mid
1.220 |
0.030
40.674 |
0.000
| 1.159 |
| 1.280 |
1.159 1.280
Age
0.029 |
0.067
0.439 |
0.663 |
| -0.105 |
| 0.164 |
-0.105 0.164
EES
–
|
| 0.096 |
0.047 |
-2.020 |
0.050 |
| -0.191 |
| -0.000 |
-0.191 -0.000
SR |
-0.074 |
0.084 |
-0.876 |
0.386 |
| -0.244 |
0.096 -0.244 0.096
G
2.552 |
0.847 |
3.012 |
0.004 |
| 0.842 |
| 4.261 |
0.842 4.261
Raise
0.834 |
0.643 |
1.299 |
0.201 |
| -0.462 |
| 2.131 |
-0.462 2.131
Deg
1.002 |
0.744 |
1.347 |
0.185 |
| -0.500 |
| 2.504 |
-0.500 2.504
Interpretation:
Do you reject or not reject the regression null hypothesis? |
Do you reject or not reject the null hypothesis for each variable? |
What is the regression equation, using only significant variables if any exist? |
What does result tell us about equal pay for equal work for males and females? |
3
Perform a regression analysis using compa as the dependent variable and the same independent |
variables as used in question 2. Show the result, and interpret your findings by answering the same questions. |
Note: be sure to include the appropriate hypothesis statements. |
4
Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not? |
Which is the best variable to use in analyzing pay practices – salary or compa? Why? |
5
Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question? |
What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test? |
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