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week 2 BUS updated assignment

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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  1. 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?
  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? 

2

>

D

ata

ompa

id

ge

ES

1

1

8 0

0 M E

2

7 0

0 M

simplfy the analysis, we will assume that jobs within each grade comprise equal work.

3

31

5 1

1

B

4

7

57

0

0

1 M E

5

16 0 5.7 1 M D

6

4

36 70

0

1 M F

– Age in years

– Appraisal rating (Employee evaluation score)

7

8 1 5.7 1 F C

(0 = male, 1 = female)

8

23 32 90 9 1

1 F A

– salary grade midpoint

9

67 49 100 10 0 4 1 M F

– job/pay grade

)

10

6

23 30 80 7 1

1 F A

(

or

)

23 1.000 23 41 100

1

1 F A

12

57 52 95 22 0 4.5 0 M E

13 42

40 30 100 2 1 4.7 0 F C

23 32 90 12 1 6 1 F A

15 24

23 32 80 8 1

1 F A

16 47

5

40

90 4 0 5.7 0 M C

17

0

57 27

3 1 3 1 F E

36

31 31 80 11 1

0 F B

19 24 1.043 23 32 85 1 0

1 M A

34

31 44 70 16 1 4.8 0 F B

21 76

67 43 95 13 0

1 M F

22 57

48 48

6 1

1 F D

23 23 1.000 23 36 65 6 1

0 F A

24 50

48 30 75 9 1 3.8 0 F D

25 24 1.043 23 41 70 4 0 4 0 M A

24 1.043 23 22 95 2 1

0 F A

27 40 1.000 40

80 7 0

1 M C

75

67 44 95 9 1

0 F F

67 52 95 5 0

0 M F

30 49

48

90 18 0

0 M D

31 24 1.043 23 29 60 4 1 3.9 1 F A
32 28

31 25 95 4 0 5.6 0 M B

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

0 F A

36 23 1.000 23 27 75 3 1 4.3 0 F A

22

23 22 95 2 1 6.2 0 F A

56

57 45 95 11 0 4.5 0 M E

35

31 27 90 6 1 5.5 0 F B

40 25

23 24 90 2 0 6.3 0 M A

41 43

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

67 42 95 20 1 5.5 0 F F

44 60 1.052 57 45 90 16 0

1 M E

45 55

48 36 95 8 1 5.2 1 F D

65

57 39 75 20 0 3.9 1 M E

47

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

0 M E

50 66

57 38 80 12 0 4.6 0 M E

ID Sal C M A E SER G Raise Deg Gen

 1 Gr
5 8 1.

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0 7 57 3 4 85 5.7 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)?
27 0.8

 70 31 52 80 3.

 9 B Note:

to
34 1.09

 6 30 75 3.6 F
66 1.

 15 42 10 16 5.5 The column labels in the table mean:
47 0.979 48 36 90 ID – Employee sample number Sal – Salary in thousands
76 1.

 13 67 12 4.5 Age EES
41 1.0

 25 40 32 100 SER – Years of service G –

Gender
23 1.000 5.8 Mid Raise – percent of last raise
77 1.1

 49 Grade Deg (0= BS\BA 1 =

MS
22 0.

 95 4.7 Gen1 Male Female Compa – salary divided by midpoint, a measure of salary that removes the impact of grade
11 19 4.8
60 1.052 This data should be treated as a sample of employees taken from a company that has about 1,000
1.0

 50 employees using a random sampling approach.
14 24 1.0

 43
1.043 4.9
1.

17 44 Mac Users: The homework in this course assumes students have Windows Excel, and
69 1.

 21 55 can load the Analysis ToolPak into their version of Excel.
18 1.1

61 5.6 The analysis tool pak has been removed from Excel for Windows, but a free third-party
4.6 tool that can be used (found on an answers Microsoft site) is:
20 1.0

96 http://www.analystsoft.com/en/products/statplusmacle
1.

134 6.3 Like the Microsoft site, I make cannot guarantee the program, but do know that
1.1

87 65 3.8 Statplus is a respected statistical packag

e. You may use other approaches or tools
3.3 as desired to complete the assignments.
1.041
26 6.2
35 3.9
28 1.119 4.4
29 72 1.074 5.4
1.020 45 4.3
0.903
33 64 1.

122
5.3
37 0.9

 56
38 0.982
39 1.129
1.086
1.075
1.149
5.2
1.145
46 1.140
62 1.087
6.6
1.157

http://www.analystsoft.com/en/products/statplusmacle

Week 1

1

2

3

      Randomly selected male being in grade E?

Why are the results different?

4

a.

b.

c.

e.

5

Week 1. Describing the dat

a.
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?
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).
What is the probability for a:
a.       Randomly selected person being a male in grade E?
b.
c.
Find:
The z score for each male salary, based on only the male salaries.
The z score for each female salary, based on only the female salaries.
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.
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?

Week 2

Week 2

1

:

salary = 45

Ho: Mean salary = 45

Ha: Mean salary =/= 45

, the second variable (Ho) is listed as the same value for every corresponding value in the data set.

Assuming Unequal

s

t-Test: Two-Sample Assuming Unequal Variances

Male Ho Female Ho
Mean 52 45 Mean 38 45
Variance

0 Variance

0

25 25 Observations 25 25

0 Hypothesized Mean Difference 0

24 df 24

t Stat

3078503

P(T<=t) one-tail

t Critical one-tail 1.7108820799

P(T<=t) two-tail

7242369

t Critical two-tail 2.0638985616

Conclusion: Do not reject Ho; mean equals 45

2

3

4

5

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.
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
Ha: Mean salary =/= 45
Note when performing a one sample test with

ANOVA
t-Test: Two-

Sample Variance
Since the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situation
316 334.6666666667
Observations
Hypothesized Mean Difference
df
t Stat 1.9689038266 -1.9132063573
P(T<=t) one-tail 0.030 0.0338621184
t Critical one-tail 1.7108820799
P(T<=t) two-tail 0.0606157006 0.067
t Critical two-tail 2.0638985616
Conclusion: Do not reject Ho; mean equals 45
Interpretation:
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?

Week 3

Week 3


For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed.

A B C D E F

Grade
Gender A B C D E F
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

salaries are equal for all grades

is not significant

A B C D E F

M

2 2 2 2 2 2 12

49 55 87 96 122

Average

48 61

33333333

Variance

0.5 24.5 2 50 0.5

F

Count 2 2 2 2 2 2 12

Sum 46 70 83

134 152

Average 23 35

67 76

Variance 2 2 0.5 24.5 8 2

Total
Count 4 4 4 4 4 4
Sum 95

Average

64

Variance

ANOVA

df MS F

Sample

1 37.5

5

0000001

Interaction

5

3.1058752391

12

Total

23

Interpretation:

Grade

Gender A B C D E F

M

F

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

Gender A B C D E F

M

F

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.
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.
2.      The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.
The salary values were randomly picked for each cell.
Ho:

Average
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
Ha: Interaction is significant
Perform analysis:
Anova: Two-Factor With Replication
SUMMARY Total
Count
Sum 153 562
24.5 2

 7.5 4

 3.5 76.5 46.

83
0.5 364.5151515

152
107 592
41.5 53.5 49.3333333333
367.3333333333
125 170 203 256 305
23.75 31.25 4

 2.5 50.75 76.25
1.5833333333 19.5833333333 9.6666666667 18.9166666667 31.3333333333 0.9166666667
Source of Variation SS P-value F crit
37.5 3.8461538462 0.0734833371 4.7472253467
Columns 7841.8333333333 1568.3666666667 160.8581196581 0.000 3.1058752391 Note: a number with an E after it (E9 or E-6, for example)
91.5 18.3 1.8769230769 0.1723082608 means we move the decimal point that number of places.
Within 117 9.75 For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456
8087.8333333333
Do we reject or not reject each of the null hypotheses? What do your conclusions mean about the population values being tested?
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.
for the intersection of M and A might be 1.043.>
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:
Hint: use mean values in the boxes.
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


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

A 0 F 41

C 0 F 77

Perform analysis:

A B C D E F Total

7 5 3 2 5 3 25

8 2 2 3 7 3 25

15 7 5 5 12 6 50

7.5 3.5 2.5 2.5 6 3 25

lighting each cell with show how the value

7.5 3.5 2.5 2.5 6 3 25

15 7 5 5 12 6 50

Interpretation:

2

Males Mean

to High

52

Females 38

Interpretation:

C 0 F 55
D 1 M 77
3

D 1 M 60

4

5

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.
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
OBSERVED
COUNT – M or 0
COUNT – F or 1
total
EXPECTED
< High
is found: row total times column total divided by
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?
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)?
St error Low
3.6587793957 44.4482793272 59.5517206728 Results are mean +/-2.064*standard error
3.6227541769 30.5226353789 45.4773646211 2.064 is t value for 95% interval
Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?
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?
How do you interpret these results in light of our question about equal pay for equal work?

Week 5

For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculations you performed.

1

2

Sal

Observations 50

ANOVA

df SS MS F

Regression 7

42

Total 49

Standard Error t Stat P-value

-11.627 3.609

Mid

0.030

0.000

1.159 1.280

Age

0.067

-0.105 0.164

EES

-0.191 -0.000

0.096 -0.244 0.096

G

0.842 4.261

Raise

-0.462 2.131

Deg

-0.500 2.504

Interpretation:

3

4

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.
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?
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
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
Significance F
17783.6554628284 2540.5222089755 377.9139268848 8.44042689148567E-36
Residual 282.3445371716 6.7224889803
18066
Coefficients Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -4.009 3.775 -1.062 0.294 -11.627 3.609
1.220 40.674 1.159 1.280
0.029 0.439 0.663 -0.105 0.164
–

 0.096 0.047 -2.020 0.050 -0.191 -0.000
SR -0.074 0.084 -0.876 0.386 -0.244
2.552 0.847 3.012 0.004 0.842 4.261
0.834 0.643 1.299 0.201 -0.462 2.131
1.002 0.744 1.347 0.185 -0.500 2.504
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?
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.
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?
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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