BUS308 Week 4

Week 4

Confidence Intervals and Chi Square (Chs 11 - 12)

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



Using our sample data, 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)?

Mean St error t value

Low

to

High

Males

Females

<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.



Interpretation:



<1 point



2



Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population.

How does this compare to the findings in week 2, question 2?

Difference St Err. T value



Low



to



High



Yes/No

Can the means be equal?



Why?



How does this compare to the week 2, question 2 result (2 sampe t-test)?

a. Why is using a two sample tool (t-test, confidence interval) a better
choice than using 2 one-sample techniques when comparing two samples?



<1 point



3



We found last week that the degree values within the population do not impact compa rates.

This does not mean that degrees are distributed evenly across the grades and genders.

Do males and females have athe same distribution of degrees by grade?

(Note: while technically the sample size might not be large enough to
perform this test, ignore this limitation for this exercise.)



What are the hypothesis statements:

Ho:

Ha:

Note: You can either use the Excel Chi-related functions or do the calculations manually.

Data input tables - graduate degrees by gender and grade level

OBSERVED

A

B

C

D

E

F

Total

M Grad

Fem Grad

Male Und

Female Und



If desired, you can do manual calculations per cell here.

A

B

C

D

E

F

M Grad

Fem Grad

Male Und

Female Und

Sum =



EXPECTED

M Grad

Fem Grad

Male Und

Female Und



For this exercise - ignore the requirement for a correction factor

for cells with expected values less than 5.



Interpretation:

What is the value of the chi square statistic:

What is the p-value associated with this value:

Is the p-value <0.05?

Do you reject or not reject the null hypothesis:

If you rejected the null, what is the Cramer's V correlation:

What does this correlation mean?

What does this decision mean for our equal pay question:



<1 point



4



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

within the population?

What are the hypothesis statements:

Ho:

Ha:



A

OBS COUNT - m

OBS COUNT - f



B



C



D



E



Do manual calculations per cell here (if desired)

A

B

C

D

E



F

M

F



F



Sum =

EXPECTED



What is the value of the chi square statistic:

What is the p-value associated with this value:

Is the p-value <0.05?

Do you reject or not reject the null hypothesis:

If you rejected the null, what is the Phi correlation:

What does this correlation mean?

What does this decision mean for our equal pay question:

<2 points 5.



How do you interpret these results in light of our question about equal pay for equal work?



ID



Salary



Compa



Midpoint



Age



1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50



66.1

25.9

35.2

55.3

49.6

78.3

42.3

22.8

78

23.3

23.6

60.8

40.6

21.7

21.8

37.4

57

33.5

23

36

76

43.7

25.3

48.9

25.8

23.3

42.3

75.2

80.9

49

24.2

27.5

63.6

28.6

22.4

23.6

24.3

63

34.8

24.3

42.8

23

75.4

60.7

57.9

62.2

62.2

70.1

61.7

61.4



1.159

0.834

1.135

0.971

1.033

1.168

1.058

0.990

1.164

1.014

1.025

1.067

1.014

0.943

0.949

0.934

1.000

1.081

1.000

1.162

1.135

0.911

1.098

1.019

1.122

1.013

1.057

1.122

1.208

1.020

1.054

0.886

1.115

0.922

0.976

1.026

1.057

1.105

1.123

1.057

1.071

0.998

1.125

1.065

1.206

1.091

1.091

1.230

1.083

1.077



57

31

31

57

48

67

40

23

67

23

23

57

40

23

23

40

57

31

23

31

67

48

23

48

23

23

40

67

67

48

23

31

57

31

23

23

23

57

31

23

40

23

67

57

48

57

57

57

57

57



34

52

30

42

36

36

32

32

49

30

41

52

30

32

32

44

27

31

32

44

43

48

36

30

41

22

35

44

52

45

29

25

35

26

23

27

22

45

27

24

25

32

42

45

36

39

37

34

41

38



Performance Service Gender Raise Degree Gender

Rating

1

85

80

75

100

90

70

100

90

100

80

100

95

100

90

80

90

55

80

85

70

95

65

65

75

70

95

80

95

95

90

60

95

90

80

90

75

95

95

90

90

80

100

95

90

95

75

95

90

95

80



8

7

5

16

16

12

8

9

10

7

19

22

2

12

8

4

3

11

1

16

13

6

6

9

4

2

7

9

5

18

4

4

9

2

4

3

2

11

6

2

5

8

20

16

8

20

5

11

21

12



0

0

1

0

0

0

1

1

0

1

1

0

1

1

1

0

1

1

0

1

0

1

1

1

0

1

0

1

0

0

1

0

0

0

1

1

1

0

1

0

0

1

1

0

1

0

0

1

0

0



5.7

3.9

3.6

5.5

5.7

4.5

5.7

5.8

4

4.7

4.8

4.5

4.7

6

4.9

5.7

3

5.6

4.6

4.8

6.3

3.8

3.3

3.8

4

6.2

3.9

4.4

5.4

4.3

3.9

5.6

5.5

4.9

5.3

4.3

6.2

4.5

5.5

6.3

4.3

5.7

5.5

5.2

5.2

3.9

5.5

5.3

6.6

4.6



0

0

1

1

1

1

1

1

1

1

1

0

0

1

1

0

1

0

1

0

1

1

0

0

0

0

1

0

0

0

1

0

1

1

0

0

0

0

0

0

0

1

0

1

1

1

1

1

0

0



M

M

F

M

M

M

F

F

M

F

F

M

F

F

F

M

F

F

M

F

M

F

F

F

M

F

M

F

M

M

F

M

M

M

F

F

F

M

F

M

M

F

F

M

F

M

M

F

M

M



Gr

E

B

B

E

D

F

C

A

F

A

A

E

C

A

A

C

E

B

A

B

F

D

A

D

A

A

C

F

F

D

A

B

E

B

A

A

A

E

B

A

C

A

F

E

D

E

E

E

E

E



The ongoing question that the weekly assignments w



Note: to simplfy the analysis, we will assume that job



The column labels in the table mean:

ID – Employee sample number

Salary – S

Age – Age in years

Performan

Service – Years of service (rounded) Gender – 0

Midpoint – salary grade midpoint

Raise – pe

Grade – job/pay grade

Degree (0=

Gender1 (Male or Female)

Compa - s



will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?



bs within each grade comprise equal work.



Salary in thousands

nce Rating - Appraisal rating (employee evaluation score)

0 = male, 1 = female

ercent of last raise

= BS\BA 1 = MS)

salary divided by midpoint

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