BUS 308 Week 2 Assignment

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)?
Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.

The column labels in the table mean:
ID – Employee sample number Sal – Salary in thousands
Age – Age in years
EES – Appraisal rating (Employee evaluation score)
SER – Years of service
G – Gender (0 = male, 1 = female)
Mid – salary grade midpoint Raise – percent of last raise
Grade – job/pay grade
Deg (0= BSBA 1 = MS)
Gen1 (Male or Female)
Compa – salary divided by midpoint, a measure of salary that removes the impact of grade
This data should be treated as a sample of employees taken from a company that has about 1,000
employees using a random sampling approach.
Mac Users: The homework in this course assumes students have Windows Excel, and
can load the Analysis ToolPak into their version of Excel.
The analysis tool pak has been removed from Excel for Windows, but a free third-party
tool that can be used (found on an answers Microsoft site) is:
http://www.analystsoft.com/en/products/statplusmacle
Like the Microsoft site, I make cannot guarantee the program, but do know that
Statplus is a respected statistical package. You may use other approaches or tools
as desired to complete the assignments.

Week 1. Describing the data.

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

5

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?
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?

W eek 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 Variances
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
334.6667
0
Observations
25
25
Observations
25
25
Hypothesized Mean Difference 0
Hypothesized Mean Difference
0
df
24
df
24
t Stat
1.968903827
t Stat
-1.91321
P(T<=t) one-tail
0.03030785
P(T<=t) one-tail
0.033862
t Critical one-tail
1.71088208
t Critical one-tail 1.710882
P(T<=t) two-tail
0.060615701
P(T<=t) two-tail
0.067724
t Critical two-tail
2.063898562
t Critical two-tail 2.063899
Conclusion: Do not
Conclusion: Do not
reject Ho; mean
reject Ho; mean
equals 45
equals 45
Males
The way that I interpret the results are that since the p-value =.061 is greater than the alpha = .05 it tells me that there is insufficient evidence to make the claim that the average salary of males is significantly different than the average for all employees.
Females
The way that I interpret the results are that since the p-value =.068 is greater than the alpha = .05 it tells me that there is insufficient evidence to make the claim that the average salary of males is significantly different than the average for all employees.

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.
t-Test : Two-sample Assuming equal variances
Male-salay

Female-salary
mean
52
38
Variance
316 334.6667
Observations
25
25
Pooled Variance
325.3333
Hypothesized mean Difference 0
degree of freedom
48
t-Stat
2.744219
0.004253
P(T ? t) one-tail
t Critical one-tail
1.677224
P(T ? t) Two-tail
0.008506
t Critical two-tail

t-Test : Two-sample Assuming Unequal variances
Male-salay emale-salary
F
mean
52
38
Variance
316 334.6667
Observations
25
25
Hypothesized mean Difference
0
degree of freedom
48
t-stat
2.744219
P(T ? t) one-tail
0.004253
t Critical one-tail
1.67724
P(T ? t) Two-tail
0.008506
t Critical two-tail
2.010635

2.010635

Based on the results of the 2-sample t-test the p-value =.008 and being less than alpha which is .05 that tells me that there is sufficient evidence that indicates the average salaries of males and females significantly different.
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.)
t-Test: Two-Sample Assuming Equal Variances

t-Test: Two-Sample Assuming UnEqual Variances

Male-compa Female-compa
Mean
1.05624
1.06872
Variance
0.007021
0.004948
Observations
25
25
Pooled Variance
0.005984
Hypothesized mean Difference
0
degree of freedom
48
t-Stat
-0.57037
P(T ? t) one-tail
0.285544
t Critical one-tail
1.677224
P(T ? t) Two-tail
0.571088
t Critical two-tail
2.010635

Male-compaemale-compa
F
Mean
1.05624 1.06872
Variance 0.007021 0.004948
Observations
25
25
Hypothesized mean 0
Difference
degree of freedom 48
t-Stat
-0.57037
P(T ? t) one-tail
0.285572
t Critical one-tail
1.677927
P(T ? t) Two-tail
0.571144
t Critical two-tail
2.011741

Based on the sample results the p-value =.571 is greater than the alpha = .05 tells me that there is insufficient
evidence to indicate the average compa’s of males and females are significantly different, which also tells me
that the male and female compass are equal.
4

What other information would you like to know to answer the question about salary equity between the genders? Why?
The other information that would be needed to answer the question is about salary equity between the
genders are, years of service, degree, performance rating, and experience. All of these attributes are important
w hen salaries are negotiated and agreed upon

5

If the salary and compa mean tests in questions 3 and 4 provide different results about male and female salary equality,
w hich would be more appropriate to use in answering the question about salary equity? Why?
What are your conclusions about equal pay at this point?
The mean test in questions 3 & 4 do give different conclusions.
The reason why, is that by using the compa it removes the impact of grade.
In my conclusions the better of the two t-test is the one which compares the comp’s.

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.
Note: Assume equal variances for all grades.
A
B
C
D
E
F

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
The salary values were randomly picked for each cell.
M
24
27
40
47
56
76
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
M
Count
Sum
Average
Variance

B

C

D

E

F

Total

2
49
24.5
0.5

2
55
27.5
0.5

2
87
43.5
24.5

2
96
48
2

2
122
61
50

2
12
153
562
76.5 46.83333
0.5 364.5152

2
46
23
2

2
70
35
2

2
83
41.5
0.5

2
107
53.5
24.5

2
134
67
8

2
12
152
592
76 49.33333
2 367.3333

F
Count
Sum
Average
Variance

Total
Count
4
4
4
4
4
4
Sum
95
125
170
203
256
305
Average
23.75
31.25
42.5
50.75
64
76.25
Variance
1.58333 19.5833 9.66667 18.9167 31.3333 0.916667
ANOVA
Source of VariationSS
Sample
37.5
Columns
7841.83
Interaction
91.5
Within
117
Total

8087.83

df

MS
F
P-value F crit
1
37.5 3.84615 0.07348 4.747225
5 1568.37 160.858 1E-010 3.105875
5
18.3 1.87692 0.17231 3.105875
12
9.75

Note: a number with an E after it (E9 or E-6, for example)
means we move the decimal point that number of places.
For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456

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?
Be sure to include the null and alternate hypothesis along with the statistical test and result.
Grade

Gender
A
B
C
D
E
F
for the intersection of M and A might be 1.043.>
M

salary values used in question 2 for a more direct comparison of the two
F
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
Hint: use mean values in the boxes.
M
F

5.

Using the results for this week, What are your conclusions about gender equal pay for equal work at this point?

Week 4
Confidence Intervals and Chi Square (Chs 11 – 12)Let’s look at some other factors that might influence pay.
For question 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.
One question we might have is if the distribution of graduate and undergraduate degrees independent of the grade the employee?
(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.
Ha: The population correlation between grade and degree is > 0
Perform analysis:
A
B
C
D
E
F
Total
OBSERVED
7
5
3
2
5
3
25
COUNT – M or 0
8
2
2
3
7
3
25
COUNT – F or 1
15
7
5
5
12
6
50
total
EXPECTED
7.5
3.5
2.5
2.5
6
3
25

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.>
1

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:
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
3.65878
44.4483
59.5517
Results are mean +/-2.064*standard error
Females
38
3.62275
30.5226
45.4774
2.064 is t value for 95% interval

2

Interpretation:
3

Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?

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?

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
SUMMARY OUTPUT

The analysis used Sal as the y (dependent variable) and
mid, age, ees, sr, g, raise, and deg as the dependent
variables (entered as a range).

Regression Statistics
Multiple R 0.992154976
R Square 0.984371497
Adjusted R Square 0.981766746
Standard Error 2.592776307
Observations
50
ANOVA
df
Regression
Residual
Total

SS
MS
F
Significance F
7 17783.66 2540.522 377.9139 8.440427E-036
42 282.3445 6.722489
49
18066

Coefficients
Intercept
-4.009
Mid
1.220
Age
0.029
EES
-0.096
SR
-0.074
G
2.552
Raise
0.834
Deg
1.002

Standard
Error
3.775
0.030
0.067
0.047
0.084
0.847
0.643
0.744

t Stat
-1.062
40.674
0.439
-2.020
-0.876
3.012
1.299
1.347

P-value
0.294
0.000
0.663
0.050
0.386
0.004
0.201
0.185

Lower 95%
-11.627
1.159
-0.105
-0.191
-0.244
0.842
-0.462
-0.500

Upper 95% Lower 95.0% Upper 95.0%
3.609
-11.627
3.609
1.280
1.159
1.280
0.164
-0.105
0.164
0.000
-0.191
0.000
0.096
-0.244
0.096
4.261
0.842
4.261
2.131
-0.462
2.131
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?