Question

For the data in the Excel file Education and Income, find 95% confidence intervals for the mean annual income of males and the mean annual income of females. Can you conclude that the mean income of one group is larger than the other?

Education and Income
Gender	Age	Level of Education	Gross Annual Income
Female	40-60	Graduate Degree	$75,000
Female	25-39	Bachelor's Degree	$47,000
Male	40-60	High School/GED	$40,000
Female	25-39	Some College	$30,000
Female	25-39	Some College	$60,000
Female	40-60	Bachelor's Degree	$80,000
Female	25-39	Bachelor's Degree	$10,000
Female	25-39	Bachelor's Degree	$43,000
Male	25-39	Bachelor's Degree	$130,000
Female	40-60	Bachelor's Degree	$89,000
Female	40-60	Graduate Degree	$50,000
Female	18-24	Some College	$13,462
Female	25-39	Bachelor's Degree	$85,000
Male	25-39	Bachelor's Degree	$60,000
Male	40-60	Graduate Degree	$200,000
Female	25-39	Associates Degree	$44,000
Male	25-39	High School/GED	$26,000
Male	25-39	Some College	$46,100
Male	25-39	Graduate Degree	$15,000
Female	25-39	Some College	$15,288
Male	25-39	Bachelor's Degree	$58,000
Female	18-24	Bachelor's Degree	$10,000
Female	25-39	Bachelor's Degree	$85,000
Male	18-24	Bachelor's Degree	$20,000

Answer 1

The 95% confidence intervals for the mean annual income of males,

The data for males is,

Gender	Gross Annual Income
Male	40000
Male	130000
Male	60000
Male	200000
Male	26000
Male	46100
Male	15000
Male	58000
Male	20000

we know that,

where, t(8 df) corresponding to 95% confidence interval is 2.3060

The 95% confidence intervals for the mean annual income of females,

The data for females is,

Gender	Gross Annual Income
Female	75000
Female	47000
Female	30000
Female	60000
Female	80000
Female	10000
Female	43000
Female	89000
Female	50000
Female	13462
Female	85000
Female	44000
Female	15288
Female	10000
Female	85000

we know that,

where, t(14 df) corresponding to 95% confidence interval is 2.1448

To test whether mean income of one group is larger than the other,

Hypothesis,

We know that,

t = 0.9153

T*(22df) = 1.7171

The corresponding p value is, p = 0.1850

Assuming the level of significance is 0.05

We fail to reject the null hypothesis, since the p value is greater than the level of significance.

Therefore, We cannot conclude that the mean income of one group is larger than the other