Question

. An experiment is conducted to compare the starting salaries of male and female college gradua find jobs. Pairs are formed es who Suppose a random sample of 8 pairs is formed in this manner and the starting annual salary of by choosing a male and a female with the same major and similar GPA. person is recorded (see table). Pair Male Female 29,000 31,600 29,800 28,500 32,600 2 4. 5 6 8 29,300 31,500 30,400 28,500 33,500 27 800 29,500 31,200 28,000 29,200 30,100 Let di Male-Female Consider the paired data t-test: Ho: Ha 0 a. Specify the critical (rejection) region. Ha: μ 0 with α = 0.05 b. Calculate the test statistic t. c. Make a decision about Ho.

Answer 1

Here this is the difference table is given below, with average difference and standard deviation of paired differences.

Pair	Male	Female	Difference(d)
1	29300	29000	300
2	31500	31600	-100
3	30400	29800	600
4	28500	28500	0
5	33500	32600	900
6	27800	28000	-200
7	29500	29200	300
8	31200	30100	1100
		Average	362.5
		Std. Dev.	471.8883

(a) HEre n = 8

dF = 8 - 1 = 7

confidence level = 0.05

test is two tailed as it is two tailed hypothesis.

t_critical = TINV(0.05, 7) =  2.3646

so here we would reject the null hypothesis when the test statistic

t < -2.3646 or t > 2.3646

(b) Here average difference = $\bar x_d$ = 362.5

standard deviation of difference = s_d = 471.8883

standard error of difference between means = se_d = s_d/sqrt(n) = 471.8883/sqrt(8) = 166.8377

Test statistic

t = $\bar x_d$/se_d = 362.5/166.8377 = 2.173

(c) so here t < t_critical so we would fail to reject the null hypothesis and conclude that there is no significant difference between salaries of males and females.