BUS308 Statistics for Managers week 4Score: 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 point> 1 Using our sample data, construct a 95% confidence interval for the populations 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



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

M Grad A B C D E F

Fem Grad M Grad

Male Und Fem Grad

Female Und Male Und

Female UndSum =

EXPECTED

M Grad For this exercise ignore the requirement for a correction factor

Fem Grad for cells with expected values less than 5.

Male Und

Female UndInterpretation:

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 Cramers 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:Do manual calculations per cell here (if desired)

A B C D E F A B C D E F

OBS COUNT m M

OBS COUNT f FSum =

EXPECTEDWhat 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?Paper details:

Lets look at some other factors that might influence pay. Complete the problems included in the resources 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 the Employee Salary Data Set and the Week 4 assignment sheet

See comments at the right of the data set.

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade

8 23 1.000 23 32 90 9 1 5.8 0 F A 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)?

10 22 0.956 23 30 80 7 1 4.7 0 F A Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.

11 23 1.000 23 41 100 19 1 4.8 0 F A

14 24 1.043 23 32 90 12 1 6 0 F A The column labels in the table mean:

15 24 1.043 23 32 80 8 1 4.9 0 F A ID Employee sample number Salary Salary in thousands

23 23 1.000 23 36 65 6 1 3.3 1 F A Age Age in years Performance Rating Appraisal rating (Employee evaluation score)

26 24 1.043 23 22 95 2 1 6.2 1 F A Service Years of service (rounded) Gender: 0 = male, 1 = female

31 24 1.043 23 29 60 4 1 3.9 0 F A Midpoint salary grade midpoint Raise percent of last raise

35 24 1.043 23 23 90 4 1 5.3 1 F A Grade job/pay grade Degree (0= BSBA 1 = MS)

36 23 1.000 23 27 75 3 1 4.3 1 F A Gender1 (Male or Female) Compa salary divided by midpoint

37 22 0.956 23 22 95 2 1 6.2 1 F A

42 24 1.043 23 32 100 8 1 5.7 0 F A

3 34 1.096 31 30 75 5 1 3.6 0 F B

18 36 1.161 31 31 80 11 1 5.6 1 F B

20 34 1.096 31 44 70 16 1 4.8 1 F B

39 35 1.129 31 27 90 6 1 5.5 1 F B

7 41 1.025 40 32 100 8 1 5.7 0 F C

13 42 1.050 40 30 100 2 1 4.7 1 F C

22 57 1.187 48 48 65 6 1 3.8 0 F D

24 50 1.041 48 30 75 9 1 3.8 1 F D

45 55 1.145 48 36 95 8 1 5.2 0 F D

17 69 1.210 57 27 55 3 1 3 0 F E

48 65 1.140 57 34 90 11 1 5.3 1 F E

28 75 1.119 67 44 95 9 1 4.4 1 F F

43 77 1.149 67 42 95 20 1 5.5 1 F F

19 24 1.043 23 32 85 1 0 4.6 1 M A

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

40 25 1.086 23 24 90 2 0 6.3 0 M A

2 27 0.870 31 52 80 7 0 3.9 0 M B

32 28 0.903 31 25 95 4 0 5.6 0 M B

34 28 0.903 31 26 80 2 0 4.9 1 M B

16 47 1.175 40 44 90 4 0 5.7 0 M C

27 40 1.000 40 35 80 7 0 3.9 1 M C

41 43 1.075 40 25 80 5 0 4.3 0 M C

5 47 0.979 48 36 90 16 0 5.7 1 M D

30 49 1.020 48 45 90 18 0 4.3 0 M D

1 58 1.017 57 34 85 8 0 5.7 0 M E

4 66 1.157 57 42 100 16 0 5.5 1 M E

12 60 1.052 57 52 95 22 0 4.5 0 M E

33 64 1.122 57 35 90 9 0 5.5 1 M E

38 56 0.982 57 45 95 11 0 4.5 0 M E

44 60 1.052 57 45 90 16 0 5.2 1 M E

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

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

6 76 1.134 67 36 70 12 0 4.5 1 M F

9 77 1.149 67 49 100 10 0 4 1 M F

21 76 1.134 67 43 95 13 0 6.3 1 M F

29 72 1.074 67 52 95 5 0 5.4 0 M F

BUS308 Statistics for Managers week 4

Score:    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 point>    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        If desired, you can do manual calculations per cell here.
M Grad                                    A     B    C    D    E    F
Fem Grad                                M Grad
Male Und                                Fem Grad
Female Und                                Male Und
Female Und

Sum =
EXPECTED
M Grad                                For this exercise – ignore the requirement for a correction factor
Fem Grad                                for cells with expected values less than 5.
Male Und
Female Und

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:

Do manual calculations per cell here (if desired)
A     B    C    D    E    F            A     B    C    D    E    F
OBS COUNT – m                                M
OBS COUNT – 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?

Paper details:
Let’s look at some other factors that might influence pay. Complete the problems included in the resources 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 the Employee Salary Data Set and the Week 4 assignment sheet
See comments at the right of the data set.
ID    Salary    Compa    Midpoint    Age    Performance Rating    Service    Gender    Raise    Degree    Gender1    Grade
8    23    1.000    23    32    90    9    1    5.8    0    F    A        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)?
10    22    0.956    23    30    80    7    1    4.7    0    F    A        Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11    23    1.000    23    41    100    19    1    4.8    0    F    A
14    24    1.043    23    32    90    12    1    6    0    F    A        The column labels in the  table mean:
15    24    1.043    23    32    80    8    1    4.9    0    F    A        ID – Employee sample number             Salary – Salary in thousands
23    23    1.000    23    36    65    6    1    3.3    1    F    A        Age – Age in years            Performance Rating  – Appraisal rating (Employee evaluation score)
26    24    1.043    23    22    95    2    1    6.2    1    F    A        Service – Years of service (rounded)            Gender:   0 = male, 1 = female
31    24    1.043    23    29    60    4    1    3.9    0    F    A        Midpoint – salary grade midpoint                Raise – percent of last raise
35    24    1.043    23    23    90    4    1    5.3    1    F    A        Grade – job/pay grade            Degree (0= BSBA 1 = MS)
36    23    1.000    23    27    75    3    1    4.3    1    F    A        Gender1 (Male or Female)            Compa – salary divided by midpoint
37    22    0.956    23    22    95    2    1    6.2    1    F    A
42    24    1.043    23    32    100    8    1    5.7    0    F    A
3    34    1.096    31    30    75    5    1    3.6    0    F    B
18    36    1.161    31    31    80    11    1    5.6    1    F    B
20    34    1.096    31    44    70    16    1    4.8    1    F    B
39    35    1.129    31    27    90    6    1    5.5    1    F    B
7    41    1.025    40    32    100    8    1    5.7    0    F    C
13    42    1.050    40    30    100    2    1    4.7    1    F    C
22    57    1.187    48    48    65    6    1    3.8    0    F    D
24    50    1.041    48    30    75    9    1    3.8    1    F    D
45    55    1.145    48    36    95    8    1    5.2    0    F    D
17    69    1.210    57    27    55    3    1    3    0    F    E
48    65    1.140    57    34    90    11    1    5.3    1    F    E
28    75    1.119    67    44    95    9    1    4.4    1    F    F
43    77    1.149    67    42    95    20    1    5.5    1    F    F
19    24    1.043    23    32    85    1    0    4.6    1    M    A
25    24    1.043    23    41    70    4    0    4    0    M    A
40    25    1.086    23    24    90    2    0    6.3    0    M    A
2    27    0.870    31    52    80    7    0    3.9    0    M    B
32    28    0.903    31    25    95    4    0    5.6    0    M    B
34    28    0.903    31    26    80    2    0    4.9    1    M    B
16    47    1.175    40    44    90    4    0    5.7    0    M    C
27    40    1.000    40    35    80    7    0    3.9    1    M    C
41    43    1.075    40    25    80    5    0    4.3    0    M    C
5    47    0.979    48    36    90    16    0    5.7    1    M    D
30    49    1.020    48    45    90    18    0    4.3    0    M    D
1    58    1.017    57    34    85    8    0    5.7    0    M    E
4    66    1.157    57    42    100    16    0    5.5    1    M    E
12    60    1.052    57    52    95    22    0    4.5    0    M    E
33    64    1.122    57    35    90    9    0    5.5    1    M    E
38    56    0.982    57    45    95    11    0    4.5    0    M    E
44    60    1.052    57    45    90    16    0    5.2    1    M    E
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
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
6    76    1.134    67    36    70    12    0    4.5    1    M    F
9    77    1.149    67    49    100    10    0    4    1    M    F
21    76    1.134    67    43    95    13    0    6.3    1    M    F
29    72    1.074    67    52    95    5    0    5.4    0    M    F

BUS308 Statistics for Managers week 4

Score:    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 point>    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        If desired, you can do manual calculations per cell here.
M Grad                                    A     B    C    D    E    F
Fem Grad                                M Grad
Male Und                                Fem Grad
Female Und                                Male Und
Female Und

Sum =
EXPECTED
M Grad                                For this exercise – ignore the requirement for a correction factor
Fem Grad                                for cells with expected values less than 5.
Male Und
Female Und

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:

Do manual calculations per cell here (if desired)
A     B    C    D    E    F            A     B    C    D    E    F
OBS COUNT – m                                M
OBS COUNT – 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?

Paper details:
Let’s look at some other factors that might influence pay. Complete the problems included in the resources 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 the Employee Salary Data Set and the Week 4 assignment sheet
See comments at the right of the data set.
ID    Salary    Compa    Midpoint    Age    Performance Rating    Service    Gender    Raise    Degree    Gender1    Grade
8    23    1.000    23    32    90    9    1    5.8    0    F    A        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)?
10    22    0.956    23    30    80    7    1    4.7    0    F    A        Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11    23    1.000    23    41    100    19    1    4.8    0    F    A
14    24    1.043    23    32    90    12    1    6    0    F    A        The column labels in the  table mean:
15    24    1.043    23    32    80    8    1    4.9    0    F    A        ID – Employee sample number             Salary – Salary in thousands
23    23    1.000    23    36    65    6    1    3.3    1    F    A        Age – Age in years            Performance Rating  – Appraisal rating (Employee evaluation score)
26    24    1.043    23    22    95    2    1    6.2    1    F    A        Service – Years of service (rounded)            Gender:   0 = male, 1 = female
31    24    1.043    23    29    60    4    1    3.9    0    F    A        Midpoint – salary grade midpoint                Raise – percent of last raise
35    24    1.043    23    23    90    4    1    5.3    1    F    A        Grade – job/pay grade            Degree (0= BSBA 1 = MS)
36    23    1.000    23    27    75    3    1    4.3    1    F    A        Gender1 (Male or Female)            Compa – salary divided by midpoint
37    22    0.956    23    22    95    2    1    6.2    1    F    A
42    24    1.043    23    32    100    8    1    5.7    0    F    A
3    34    1.096    31    30    75    5    1    3.6    0    F    B
18    36    1.161    31    31    80    11    1    5.6    1    F    B
20    34    1.096    31    44    70    16    1    4.8    1    F    B
39    35    1.129    31    27    90    6    1    5.5    1    F    B
7    41    1.025    40    32    100    8    1    5.7    0    F    C
13    42    1.050    40    30    100    2    1    4.7    1    F    C
22    57    1.187    48    48    65    6    1    3.8    0    F    D
24    50    1.041    48    30    75    9    1    3.8    1    F    D
45    55    1.145    48    36    95    8    1    5.2    0    F    D
17    69    1.210    57    27    55    3    1    3    0    F    E
48    65    1.140    57    34    90    11    1    5.3    1    F    E
28    75    1.119    67    44    95    9    1    4.4    1    F    F
43    77    1.149    67    42    95    20    1    5.5    1    F    F
19    24    1.043    23    32    85    1    0    4.6    1    M    A
25    24    1.043    23    41    70    4    0    4    0    M    A
40    25    1.086    23    24    90    2    0    6.3    0    M    A
2    27    0.870    31    52    80    7    0    3.9    0    M    B
32    28    0.903    31    25    95    4    0    5.6    0    M    B
34    28    0.903    31    26    80    2    0    4.9    1    M    B
16    47    1.175    40    44    90    4    0    5.7    0    M    C
27    40    1.000    40    35    80    7    0    3.9    1    M    C
41    43    1.075    40    25    80    5    0    4.3    0    M    C
5    47    0.979    48    36    90    16    0    5.7    1    M    D
30    49    1.020    48    45    90    18    0    4.3    0    M    D
1    58    1.017    57    34    85    8    0    5.7    0    M    E
4    66    1.157    57    42    100    16    0    5.5    1    M    E
12    60    1.052    57    52    95    22    0    4.5    0    M    E
33    64    1.122    57    35    90    9    0    5.5    1    M    E
38    56    0.982    57    45    95    11    0    4.5    0    M    E
44    60    1.052    57    45    90    16    0    5.2    1    M    E
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
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
6    76    1.134    67    36    70    12    0    4.5    1    M    F
9    77    1.149    67    49    100    10    0    4    1    M    F
21    76    1.134    67    43    95    13    0    6.3    1    M    F
29    72    1.074    67    52    95    5    0    5.4    0    M    F