Question

Please complete the following problems. Show as much work as you can, and complete the problems as neatly as possible. The x in [x] after each problem denotes the point value.

For each problem, perform the following steps. Assume that all variables are normally or approximately normally distributed.

1. State the hypothesis and identify the claim.

2. Find the critical value(s).

3. Compute the test value.

4. Make the decision.

5. Summarize the results.

1. The average yearly earnings of male college students (with at least a bachelor’s degree) are $58,500 for men ages 25 to 34. The average yearly earning of female college graduates with the same qualifications are $49,339. Based on the results below, can it be concluded that there is a difference in mean earnings between male and female college graduates? Use the 0.01 level of significance. [4]

	Male	Female
Sample mean	$59,235	$52,487
Population standard deviation	8,945	10,125
Sample size	40	35

Answer 1

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.576 and 2.576.
Hence reject H0 if z < -2.576 or z > 2.576

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(80013025/40 + 102515625/35)
sp = 2220.2125

Test statistic,
z = (x1bar - x2bar)/sp
z = (59235 - 52487)/2220.2125
z = 3.04

reject null hypothesis.

There is sufficient evidence to conclude that there is a difference in mean earnings between male and female college graduates