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
50.2	49.0
59.8	49.2
55.3	54.1
57.2	54.9
53.2	50.9
56.0	52.6
50.9	50.7
59.5	54.9
58.0	50.8
52.9	48.9

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

  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.

(b)

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

Public Accountantssample median=$

Financial Plannerssample median=$

Answer 1

a) W=82.5

(i) For H₀: Median salary for public accountants − Median salary for financial planners = 0

           H₁: Median salary for public accountants − Median salary for financial planners 0

Conclusion:

At 0.05 level of significance,since p value=0.01549<0.05,we conclude to reject H_0. Therefore ,there is difference between Median salary for public accountants and Median salary for financial planners.

(ii) For H₀: Median salary for public accountants − Median salary for financial planners = 0

           H₁: Median salary for public accountants − Median salary for financial planners < 0

Conclusion:

At 0.05 level of significance,since p value=0.9937>0.05,we conclude not to reject H_0. Therefore ,there is no difference between Median salary for public accountants and Median salary for financial planners.

(iii) For H₀: Median salary for public accountants − Median salary for financial planners = 0

            H₁: Median salary for public accountants − Median salary for financial planners > 0

Conclusion:

At 0.05 level of significance,since p value=0.007743<0.05,we conclude to reject H_0. Therefore ,there is difference between Median salary for public accountants and Median salary for financial planners.

b)

Public Accountants sample median=$55.65

Financial Planners sample median=$50.85