Question

This assignment is about correlations and test of hypothesis. For each test of hypothesis scenario, (a) formulate the null and alternative hypotheses, (b) indicate the test used, (c) state the p-value from the test results, and (d) provide your conclusion. In your conclusion, give a reason for rejecting or not rejecting the null and clearly state what it means in the context of the problem.

Are there significant differences in current salary for men and women?

Female	Male
$21,900.00	$57,000.00
$27,900.00	$45,000.00
$24,000.00	$36,000.00
$30,300.00	$28,350.00
$35,100.00	$103,750.00
$26,250.00	$60,375.00
$38,850.00	$32,550.00
$24,000.00	$135,000.00
$16,950.00	$36,150.00
$23,550.00	$110,625.00
$30,000.00	$42,000.00
$54,000.00	$92,000.00
$26,400.00	$31,350.00
$33,900.00	$23,250.00
$34,800.00	$60,000.00
$51,000.00	$73,750.00
$24,300.00	$26,850.00
$25,050.00	$33,900.00
$16,200.00	$28,050.00
$25,950.00	$30,900.00
$31,500.00	$22,500.00
$31,650.00	$21,900.00
$33,300.00	$78,125.00
$38,550.00	$45,250.00
$22,350.00	$41,100.00
$26,700.00	$25,950.00
$25,050.00	$72,500.00
$33,300.00	$40,200.00
$46,875.00	$60,625.00
$17,100.00	$39,900.00
$24,000.00	$97,000.00
$27,450.00	$31,650.00
$18,450.00	$33,450.00
$34,500.00	$24,300.00
$36,000.00	$31,500.00
$27,150.00	$27,300.00
$23,100.00	$30,900.00
$19,800.00	$26,700.00
$24,000.00	$43,950.00
$22,350.00	$25,800.00
$23,100.00	$35,250.00
$26,700.00	$26,700.00
$24,900.00	$52,650.00
$19,650.00	$45,625.00
$22,050.00	$26,700.00
$25,500.00	$69,250.00
$23,100.00	$31,950.00
$17,100.00	$26,250.00
$19,650.00	$25,200.00
$22,350.00	$39,300.00
$23,400.00	$70,875.00
$19,950.00	$51,250.00
$43,000.00	$67,500.00
	$29,340.00
	$39,600.00
	$29,100.00
	$27,300.00
	$34,620.00
	$80,000.00
	$25,350.00
	$22,500.00
	$40,200.00
	$68,125.00
	$52,125.00
	$21,300.00
	$40,200.00
	$33,900.00

Answer 1

For Female :

Sample mean using excel function AVERAGE(), x̅1 = 27623.1

Sample standard deviation using excel function STDEV.S, s1 = 8325.97

Sample size, n1 = 53

For Male :

Sample mean using excel function AVERAGE(), x̅2 = 45068.8

Sample standard deviation using excel function STDEV.S, s2 = 24014

Sample size, n2 = 67

a)

Null and Alternative hypothesis:

Ho : µ1 = µ2

H1 : µ1 ≠ µ2

b)
We will use a two sample unpooled t test.

c)

Test statistic:

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2)

= (27623.1132 - 45068.806)/√(8325.9728²/53 + 24014.049²/67) = -5.5404

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 85.0893 = 85

p-value =T.DIST.2T(-5.5404, 85) = 0.0000

d)

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that there is significant differences in current salary for men and women.