The average yearly earnings of male college graduates(with at least a bachelor's degree) are $59500 for men aged 25 to 34. The average yearly earnings of female college graduates with the same qualification are $49,839. 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 0.10 level of significance. Which is the correct test value?

Step-by-step explanation:

The question is incomplete. The complete question is:

The average yearly earnings of male college graduates (with at least a bachelor's degree) are $58,000 for men aged 25 to 34. The average yearly earnings 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.

sample mean: men $59,235 women $52,487

population standard deviation: men 8,945 women 10,125

sample size: men 40 women 35

a. state hypothesis

b. find the critical value(s)

c. compute the test value

d. make the decision

e. summarize the results

Solution:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean yearly earnings of male college graduates and μ2 be the mean yearly earnings of female college graduates.

The random variable is μ1 - μ2 = difference in the mean average earnings between male and female graduates.

a) We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 59235

x2 = 59487

s1 = 8945

s2 = 10125

n1 = 40

n2 = 35

t = (59235 - 59487)/√(8945²/40 + 10125²/35)

t = - 0.11

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8945²/40 + 10125²/35]²/[(1/40 - 1)(8945²/40)² + (1/35 - 1)(10125²/35)²] = 24298427164944.27/354925314702.92865

df = 68

c) We would determine the probability value from the t test calculator. It becomes

p value = 0.91

d) Since alpha, 0.1 > than the p value, 0.91, then we would fail to reject the null hypothesis.

e) We can conclude that at 10% level of significance, there is no difference in mean earnings between male and female college graduates.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb