Statistics

Statistics
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? ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr
1 66.1 1.159 57 34 85 8 0 5.7 0 M 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)?
2 25.9 0.834 31 52 80 7 0 3.9 0 M B Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3 35.2 1.135 31 30 75 5 1 3.6 1 F B
4 55.3 0.971 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 49.6 1.033 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 78.3 1.168 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating – Appraisal rating (employee evaluation score)
7 42.3 1.058 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 22.8 0.990 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 78 1.164 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 23.3 1.014 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa – salary divided by midpoint
11 23.6 1.025 23 41 100 19 1 4.8 1 F A
12 60.8 1.067 57 52 95 22 0 4.5 0 M E
13 40.6 1.014 40 30 100 2 1 4.7 0 F C
14 21.7 0.943 23 32 90 12 1 6 1 F A
15 21.8 0.949 23 32 80 8 1 4.9 1 F A
16 37.4 0.934 40 44 90 4 0 5.7 0 M C
17 57 1.000 57 27 55 3 1 3 1 F E
18 33.5 1.081 31 31 80 11 1 5.6 0 F B
19 23 1.000 23 32 85 1 0 4.6 1 M A
20 36 1.162 31 44 70 16 1 4.8 0 F B
21 76 1.135 67 43 95 13 0 6.3 1 M F
22 43.7 0.911 48 48 65 6 1 3.8 1 F D
23 25.3 1.098 23 36 65 6 1 3.3 0 F A
24 48.9 1.019 48 30 75 9 1 3.8 0 F D
25 25.8 1.122 23 41 70 4 0 4 0 M A
26 23.3 1.013 23 22 95 2 1 6.2 0 F A
27 42.3 1.057 40 35 80 7 0 3.9 1 M C
28 75.2 1.122 67 44 95 9 1 4.4 0 F F
29 80.9 1.208 67 52 95 5 0 5.4 0 M F
30 49 1.020 48 45 90 18 0 4.3 0 M D
31 24.2 1.054 23 29 60 4 1 3.9 1 F A
32 27.5 0.886 31 25 95 4 0 5.6 0 M B
33 63.6 1.115 57 35 90 9 0 5.5 1 M E
34 28.6 0.922 31 26 80 2 0 4.9 1 M B
35 22.4 0.976 23 23 90 4 1 5.3 0 F A
36 23.6 1.026 23 27 75 3 1 4.3 0 F A
37 24.3 1.057 23 22 95 2 1 6.2 0 F A
38 63 1.105 57 45 95 11 0 4.5 0 M E
39 34.8 1.123 31 27 90 6 1 5.5 0 F B
40 24.3 1.057 23 24 90 2 0 6.3 0 M A
41 42.8 1.071 40 25 80 5 0 4.3 0 M C
42 23 0.998 23 32 100 8 1 5.7 1 F A
43 75.4 1.125 67 42 95 20 1 5.5 0 F F
44 60.7 1.065 57 45 90 16 0 5.2 1 M E
45 57.9 1.206 48 36 95 8 1 5.2 1 F D
46 62.2 1.091 57 39 75 20 0 3.9 1 M E
47 62.2 1.091 57 37 95 5 0 5.5 1 M E
48 70.1 1.230 57 34 90 11 1 5.3 1 F E
49 61.7 1.083 57 41 95 21 0 6.6 0 M E
50 61.4 1.077 57 38 80 12 0 4.6 0 M E