BUS308 Statics Problem Set WorkSheet

Please complete the statics problem worksheet for week’s 1-4.  Due by tomorrow.

Must make sure to answer all questions using excel formula not numeric values

2

>

D a

ta

ompa-ratio

idpoint

ge

another page to make changes

1

8 0

0 M

2

0

2

7 0

0 M

3

31

5 1

1

B

4

7

0

0

1 M E

5

.7

48

16 0 5.7 1 M D

6

6

36

12 0

1 M F

– Age in years

7

.6

8 1 5.7 1 F C

8

.6

23 32 90 9 1

1 F A

– salary grade midpoint

9

67

100 10 0 4 1 M F

10

.5

23 30 80 7 1

1 F A

or

)

.1

23 41 100

1 4.8 1 F A

12

.3

57 52

22 0 4.5 0 M E

13

40 30 100 2 1 4.7 0 F C

14

23 32 90 12 1 6 1 F A

23 32 80 8 1

1 F A

16

.7

40 44 90 4 0 5.7 0 M C

17

57

3 1 3 1 F E

18

.9

31 31 80 11 1

0 F B

19

23 32 85 1 0

1 M A

20

.4

31 44 70 16 1 4.8 0 F B

67

95 13 0

1 M F

22

48 48

6 1 3.8 1 F D

23

.1

23 36 65 6 1

0 F A

24

48 30 75 9 1 3.8 0 F D

25

23 41 70 4 0 4 0 M A

23 22 95 2 1

0 F A

27

0.980 40 35 80 7 0 3.9 1 M C

28

67 44 95 9 1 4.4 0 F F

67 52 95 5 0 5.4 0 M F

30 48.6

48

90 18 0 4.3 0 M D

31

23 29

4 1 3.9 1 F A

32

31 25 95 4 0 5.6 0 M B

33 58 1.018 57 35 90 9 0 5.5 1 M E
34 27

31 26 80 2 0 4.9 1 M B

35 23

23 23 90 4 1

0 F A

36 23

23 27 75 3 1 4.3 0 F A

23 22 95 2 1 6.2 0 F A

57 45 95 11 0 4.5 0 M E

39 35

31 27 90 6 1 5.5 0 F B

40

23 24 90 2 0 6.3 0 M A

41

1.013 40 25 80 5 0 4.3 0 M C

42

23 32 100 8 1 5.7 1 F A

43 76

67 42 95 20 1 5.5 0 F F

44

57 45 90 16 0

1 M E

45

48 36 95 8 1 5.2 1 F D

46

57 39 75 20 0 3.9 1 M E

57 37 95 5 0 5.5 1 M E

48

57 34 90 11 1 5.3 1 F E

49

57 41 95 21 0

0 M E

57 38 80 12 0 4.6 0 M E

																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										ID	Salary									C																										M																			A	Performance Rating	Service		Gender		Raise		Degree	Gender																																																								1	Grade	Do not manipuilate Data set on this page, copy	to
							5						8	1.																																																																				0		18	5				7									3												4		85					5.7															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)?
	28	0.							9									31			52								80				3.9										B	Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3		3.8	1.089					30				75	3.					6																																		F
6		4.8	1.		13											57			42					10					16					5.5	The column labels in the table mean:
							48	1.0	14					36									90	ID – Employee sample number	Salary – Salary in thousands
7	5.4	1.				12						67			70			4.5		Age	Performance Rating – Appraisal rating (employee evaluation score)
				41	1.0		39						40							32			100	Service – Years of service (rounded)	Gender – 0 = male, 1 = female
																			23	1.028	5.8			Midpoint	Raise – percent of last raise
73.8	1.102		49	Grade – job/pay grade	Degree (0= BS\BA 1 = MS)
				22		0.980		4.7	Gender1 (					Male					Female	Compa-ratio – salary divided by midpoint
			11			24	1.0	46		19
	58	1.023												95
41.4	1.0				35
23.2	1.008
15	22.5	0.978		4.9
				44	1.1	17
63.8	1.1			20					27	55
		34	1.127		5.6
24.9	1.083		4.6
	33	1.0	76
	21	73.5	1.097		43		6.3
51.4	1.071		65
			25	1.090	3.3
	48.6		1.013
2	4.4	1.062
	26	2			4.3	1.058		6.2
39.2
75.8	1.131
	29	76.3	1.139
1.012				45
23.4		1.018	60
27.5	0.886
0.871
0.998		5.3
1.001
	37	23.6	1.026
	38	60.8	1.066
1.129
24.3	1.056
40.5
22.6	0.982
1.134
63.1	1.107		5.2
52.9	1.103
59.1	1.036
47	62.6	1.099
67.4	1.183
58.4	1.025	6.6
50	61.4	1.077

Week 1

1

to columns T and U at the right.

light the mean, sample standard deviation, and range.

Male Female
2

Midpoint
3

Male Female

What is the normal curve z value for each midpoint within overall range?

4

For full credit, show the excel formulas in each cell rather than simply the numerical answer.

Male Female

5

Week 1: Descriptive Statistics, including Probability
While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will focus on
examining the issue using the salary measur	e.
The purpose of this assignmnent is two fold:
1. Demonstrate mastery with Excel tools.
2. Develop descriptive statistics to help examine the question.
3. Interpret descriptive outcomes
The first issue in examining salary data to determine if we – as a company – are paying males and females equally for doing equal work is to develop some
descriptive statistics to give us something to make a preliminary decision on whether we have an issue or not.
Descriptive Statistics: Develop basic descriptive statistics for Salary
The first step in analyzing data sets is to find some summary descriptive statistics for key variables.
Suggestion: Copy the gender1 and salary columns from the Data ta			b
Then use Data Sort (by gender1) to get all the male and female salary values grouped together.
	a.	Use the Descriptive Statistics function in the Data Analysis tab	Place Excel outcome in Cell K19
to develop the descriptive statistics summary for the overall
group’s overall salary. (Place K19 in output range.)
	High
b.	Using Fx (or formula) functions find the following (be sure to show the formula
and not just the value in each cell) asked for salary statistics for each gender:
Mean:
Sample Standard Deviation:
Range:
Develop a 5-number summary for the overall, male, and female SALARY variable.
For full credit, use the excel formulas in each cell rather than simply the numerical answer.
Overall	Males	Females
Max
3rd Q
1st Q
Min
Location Measures: comparing Male and Female midpoints to the overall Salary data range.
	For full credit, show the excel formulas in each cell rather than simply the numerical answer.
Using the entire Salary range and the M and F midpoints found in Q2
a. What would each midpoint’s percentile rank be in the overall range?	Use Excel’s =PERCENTRANK.EXC function
	b.	Use Excel’s =STANDARDIZE function
Probability Measures: comparing Male and Female midpoints to the overall Salary data range
Using the entire Salary range and the M and F midpoints found in Q2, find
a. The Empirical Probability of equaling or exceeding (=>) that value for	Show the calculation formula = value/50 or =countif(range,”>=”&cell)/50
b. The Normal curve Prob of => that value for each group	Use “=1-NORM.S.DIST” function
Note: be sure to use the ENTIRE salary range for part a when finding the probability.
Conclusions: What do you make of these results?	Be sure to include findings from this week’s lectures as well.
In comparing the overall, male, and female outcomes, what relationship(s) see, to exist between the data sets?
			Your findings:
			The lecture’s related findings:
			Overall conclusion:
What does this suggest about our equal pay for equal work question?

Week 2

1

a

b

Step 1:

– place test function in cell k10

2

a What is the data input ranged used for this question:

b

Why:
c. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:

Step 5:

Step 6: Conclusion and Interpretation
What is the p-value:

What is your decision: REJ or NOT reject the null?

Why?

3

a What is the data input ranged used for this question:

b Does this question need a one or two-tail hypothesis statement and test?
Why:
c. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:

Step 5:

Step 6: Conclusion and Interpretation
What is the p-value:

What is your decision: REJ or NOT reject the null?
Why?

4

Your findings:
The lecture’s related findings:
Overall conclusion:

Week 2: Identifying Significant Differences – part 1

To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located

or showing the excel formula in each cell.

Be sure to copy the appropriate data columns from the data tab to the right for your use this week.

As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders involves equality – are they the same or different?

What we do, depends upon our findings.

As with the compa-ratio lecture example, we want to examine salary variation within the groups – are they equal?

Use Cell K10 for the Excel test outcome location.

What is the data input ranged used for this question:

Which is needed for this question: a one- or two-tail hypothesis statement and test ?

Answer:

Why:

c.

Ho:

Ha:

Step 2:

Significance (Alpha):

Step 3:

Test Statistic and test:

Why this test?

Step 4:

Decision rule:

Step 5:

Conduct the test

Step 6:

Conclusion and Interpretation

What is the p-value:

What is your decision: REJ or NOT reject the null?

Why?

What is your conclusion about the variance in the population for male and female salaries?

Once we know about variance quality, we can move on to means: Are male and female average salaries equal?

Use Cell K35 for the Excel test outcome location.

(Regardless of the outcome of the above F-test, assume equal variances for this test.)

Does this question need a one or two-tail hypothesis statement and test?

Conduct the test – place test function in cell K35

What is your conclusion about the means in the population for male and female salaries?

Education is often a factor in pay differences.

Do employees with an advanced degree (degree = 1) have higher average salaries?

Use Cell K60 for the Excel test outcome location.

Note: assume equal variance for the salaries in each degree for this question.

Conduct the test – place test function in cell K60

Is the t value in the t-distribution tail indicated by the arrow in the Ha claim?

What is your conclusion about the impact of education on average salaries?

Considering both the compa-ratio information from the lectures and your salary information, what conclusions can you reach about equal pay for equal work?

Why – what statistical results support this conclusion?

Week 3

A B C D E F

To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located

or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
1

a What is the data input ranged used for this question:

Ho:

Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:

Step 5:

Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?

2

to High

Why?

B-E

3

a What is the data input ranged used for this question:

b. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):

Step 3: Test Statistic and test:

Why this test? A B C D E F

Step 4: Decision rule: Male 0
Step 5:

Female 0

0 0 0 0 0 0 0

Step 6: Conclusion and Interpretation

What is the p-value: A B C D E F
What is your decision: REJ or NOT reject the null? Male 0
Why? Female 0
What is your conclusion about the means in the population for male and female salaries? Sum: 0 0 0 0 0 0 0
4

Your findings:
The lecture’s related findings:
Overall conclusion:
Why – what statistical results support this conclusion?

Week 3: Identifying Significant Differences – part 2	Data Input Table:	Salary Range Groups
Group name:
List salaries within each grade
A good pay program will have different average salaries by grade. Is this the case for our company?
	Use Cell K08 for the Excel test outcome location.
Note: assume equal variances for each grade, even though this may not be accurate, for purposes of this question.
	b. Step 1:
Conduct the test – place test function in cell K08
What is your conclusion about the means in the population for grade salaries?
If the null hypothesis in question 1 was rejected, which pairs of means differ?
(Use the values from the ANOVA table to complete the follow table.)
Groups Compared	Mean Dif	f.	T value used	+/- Term	Low	Difference Significant?
A-B
A-C
A-D
A-E
A-F
B-C
B-D
	B-E
C-D
C-E
C-F
D-E
D-F
E-F
One issue in salary is the grade an employee is in – higher grades have higher salaries.
This suggests that one question to ask is if males and females are distributed in a similar pattern across the salary grades?
Use Cell K54 for the Excel test outcome location.
Place the actual distribution in the table below.
Sum
Conduct the test – place test function in cell K54
	Sum:
Place the expected distribution in the table below.
What implications do this week’s analysis have for our equal pay question?

Week 4

To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located
or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.

1

Use Cell K08 for the Excel test outcome location.

What is the data input ranged used for this question:

Are there any surprises – correlations you though would be significant and are not, or non significant correlations you thought would be?

2

a. What is the data input ranged used for this question:
b.

Ho:

Ha:

Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5:

Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
c.

Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:

Step 5: Conduct the test

Step 6: Conclusion and Interpretation

Midpoint Age

Raise Gender Degree

d.

e.

f.

3

4

Your findings:
The lecture’s related findings:
Overall conclusion:

5

Week 4: Identifying relationships – correlations and regression
What is the correlation between and among the interval/ratio level variables with salary? (Do not include compa-ratio in this question.)
a. Create the correlation table.
i.
ii.	Create a correlation table in cell K08.
b. Technically, we should perform a hypothesis testing on each correlation to determine
if it is significant or not. However, we can be faithful to the process and save some
time by finding the minimum correlation that would result in a two tail rejection of the null.
We can then compare each correlation to this value, and those exceeding it (in either a
positive or negative direction) can be considered statistically significant.
i. What is the t-value we would use to cut off the two tails?	T =
ii. What is the associated correlation value related to this t-value? r =
c. What variable(s) is(are) significantly correlated to salary?
	d.
e. Why does or does not this information help answer our equal pay question?
Perform a regression analysis using salary as the dependent variable and all of the variables used in Q1. Add the
two dummy variables – gender and education – to your list of independent variables. Show the result, and interpret your findings by answering the following questions.
Suggestion: Add the dummy variables values to the right of the last data columns used for Q1.
What is the multiple regression equation predicting/explaining salary using all of our possible variables except compa-ratio?
Step 1: State the appropriate hypothesis statements:	Use Cell M34 for the Excel test outcome location.
Conduct the test – place test function in cell M34
What is your conclusion about the factors influencing the population salary values?
If we rejected the null hypothesis, we need to test the significance of each of the variable coefficients.
Step 1: State the appropriate coefficient hypothesis statements:	(Write a single pair, we will use it for each variable separately.)
Note, in this case the test has been performed and is part of the Regression output above.
Place the t and p-values in the following table
Identify your decision on rejecting the null for each variable. If you reject the null, place the coefficient in the table.
Perf. Rat.	Seniority
t-value:
P-value:
Rejection Decision:
If Null is rejected, what is the variable’s coefficient value?
Using the intercept coefficient and only the significant variables, what is the equation?
Salary =
Is gender a significant factor in salary?
Regardless of statistical significance, who gets paid more with all other things being equal?
How do we know?
After considering the compa-ratio based results in the lectures and your salary based results, what else would you like to know
before answering our question on equal pay? Why?
Between the lecture results and your results, what is your answer to the question
of equal pay for equal work for males and females? Why?
What does regression analysis show us about analyzing complex measures?