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:
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?
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:
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:
5. How do you interpret these results in light of our question about equal pay for equal work?
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= BS\BA 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