Question

MBA_Salary table contains the annual salaries, in thousands of dollars, earned by individuals who graduated with MBAs in 2015 and 2016 from a certain business school in Canada. We would like to determine whether the distribution of salaries for 2015 MBA graduates is higher than for 2016 MBA graduates. a) Create a boxplot and compare the distribution of salaries for 2015 and 2016 graduates. b) Perform the appropriate non-parametric test at a 5% significance level to determine whether the salary for 2015 graduates is higher than for 2016 graduates. State the hypotheses clearly and show your manual calculation for all the relevant steps in the test. c) Use Excel to perform the appropriate non-parametric test in part (b). How does the result from Excel compare with your conclusion in part (b).

2015 Graduates ($)	2016 Graduates ($)
64.9	59.4
48	74.8
62.5	55
58.5	34.2
56.5	68
98.1	78.8
36.6	53.9
55.5	40.6
70.7	64.6
52.9	44.4
41.6	87.8
82.7	67.4
96.8	46.8
46.9	49.3
	36.2

Answer 1

a) Create a boxplot and compare the distribution of salaries for 2015 and 2016 graduates.

The distribution of salaries for 2015 and 2016 graduates is almost similar.

b) Perform the appropriate non-parametric test at a 5% significance level to determine whether the salary for 2015 graduates is higher than for 2016 graduates. State the hypotheses clearly and show your manual calculation for all the relevant steps in the test.

η₁: median of 2015 Graduates ($)

η₂: median of 2016 Graduates ($)

Difference: η₁ - η₂

Descriptive Statistics

Sample	N	Median
2015 Graduates ($)	15	56.5
2016 Graduates ($)	14	57.2

Estimation for Difference

Difference	Lower Bound for Difference	Achieved Confidence
0.4	-11.4	95.35%

The hypothesis being tested is:

Null hypothesis	H₀: η₁ - η₂ = 0
Alternative hypothesis	H₁: η₁ - η₂ > 0

W-Value	P-Value
227.00	0.474

The p-value is 0.474.

Since the p-value (0.474) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the salary for 2015 graduates is higher than for 2016 graduates.

c) Use Excel to perform the appropriate non-parametric test in part (b). How does the result from Excel compare with your conclusion in part (b).

n	sum of ranks
15	227	2015 Graduates ($)
14	208	2016 Graduates ($)
29	435	total
	225.000	expected value
	22.913	standard deviation
	0.087	z
	.4652	p-value (one-tailed, upper)

The result is the same.