A 95% confidence interval for the mean salary difference between genders in the sample data is calculated as $4.77 to $25.35. A two-sample t-test indicates the means are not equal, as the p-value is 0.005. Using a two-sample t-test is better than two one-sample tests when comparing samples, as it directly tests if a difference exists between the sample means rather than just providing individual confidence intervals.
2. Using our sample data, construct a 95 confidence interval for th.pdf
1. 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
Can the means be equal? Yes or No. Why?
Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-
sample techniques when comparing two samples?
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
18. E
50
61.4
1.077
57
38
80
12
0
4.6
0
M
E
Difference
St Err.
T value
Low
to
High
Solution
Two-sample T for Salary
Gender N Mean StDev SE Mean
0 25 52.3 18.6 3.7
1 25 37.2 17.5 3.5
Difference = mu (0) - mu (1)
Estimate for difference: 15.06
95% CI for difference: (4.77, 25.35)
T-Test of difference = 0 (vs not =): T-Value = 2.94 P-Value = 0.005 DF = 48
Difference = 15.06
standard error of difference between means = 5.107
T value = 2.94
Low = 4.77
19. High =25.35
No, The means are not equal . ( since P-value is very low i.e. 0005)
We use two sample t-test to the average salary differences between the two genders. This gives
whether there is truly difference exists between the genders . If we use one sample individual
test, then this test gives the individual averages confidence interval , from which we can't
interpret the difference of their averages.