Question

Samples of starting annual salaries for individuals entering the public accounting and financial planning professions follow. Annual salaries are shown in thousands of dollars.

Public Accountant	Financial Planner
51.2	48.0
59.8	49.2
55.3	53.1
57.2	55.9
54.2	51.9
56.0	52.6
51.9	49.7
60.5	53.9
57.0	51.8
50.9	49.9

(a)

Use a 0.05 level of significance and test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners.

State the null and alternative hypotheses.

H₀: Median salary for public accountants − Median salary for financial planners ≤ 0
H_a: Median salary for public accountants − Median salary for financial planners > 0H₀: The two populations of salaries are not identical.
H_a: The two populations of salaries are identical.     H₀: The two populations of salaries are identical.
H_a: The two populations of salaries are not identical.H₀: Median salary for public accountants − Median salary for financial planners > 0
H_a: Median salary for public accountants − Median salary for financial planners = 0H₀: Median salary for public accountants − Median salary for financial planners ≥ 0
H_a: Median salary for public accountants − Median salary for financial planners < 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.     Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.

(b)

What are the sample median annual salaries (in $) for the two professions?

Public Accountants sample median = $

Financial Planners sample median = $

Answer 1

a)

H0: The two populations of salaries are identical.
Ha: The two populations of salaries are not identical

sample 1	sample 2	rank for sample 1	rank for sample 2
51.2	48	6	1
59.8	49.2	19	2
55.3	53.1	14	11
57.2	55.9	18	15
54.2	51.9	13	8.5
56	52.6	16	10
51.9	49.7	8.5	3
60.5	53.9	20	12
57	51.8	17	7
50.9	49.9	5	4

sample 1      
sample size ,    n1 =    10
sum of ranks ,    R1 =    136.5
      
sample 2      
sample size ,    n2 =    10
sum of ranks ,   R2 =    73.5

value of the test statistic,      
W=sum of ranks for smaller sample size =       136.5
      
mean ,µ =    n1(n1+n2+1)/2 =    105
      
std dev,σ =    √(n1*n2*(n1+n2+1)/12) =   13.2288
      
Z-stat =    (R - µ)/σ =    2.3812
      
Z*, Z critical value =        1.960
      
P-value =        0.0173
Conclusion:         P-value<α , Reject null hypothesis

Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.

b)

Public Accountants sample median =0.5(n+1)th value of sorted data = 5.5th of sorted data = $55.65

Financial Planners sample median = 0.5(n+1)th value of sorted data = 5.5th of sorted data = $51.85