Question

A large corporation sends many of its first-level managers to an off-site supervisory skills training course. Four different management development centers offer this course. The director of human resources would like to know whether there is a difference among the quality of training provided at the four centers. An independent random sample of five employees was chosen from each training center. The employees were then ranked 1 to 20 in terms of supervisory skills. A rank of 1 was assigned to the employee with the best supervisory skills. Suppose the ranks are as shown.

Course
A	B	C	D
5	1	20	16
13	9	17	4
6	3	7	14
15	2	18	8
11	12	19	10

Use α = 0.05 and test whether there is a significant difference among the quality of training provided by the four programs.

State the null and alternative hypotheses.

H₀: Median_A ≠ Median_B ≠ Median_C ≠ Median_D
H_a: Median_A = Median_B = Median_C = Median_DH₀: Median_A = Median_B = Median_C = Median_D
H_a: Median_A > Median_B < Median_C > Median_D    H₀: There is no difference in the quality of the training for the programs.
H_a: There is a difference in the quality of the training for the programs.H₀: Median_A = Median_B = Median_C = Median_D
H_a: Median_A ≠ Median_B ≠ Median_C ≠ Median_DH₀: There is a difference in the quality of the training for the programs.
H_a: There is no difference in the quality of the training for the programs.

Find the value of the test statistic. (Round your answer to two decimal places.)

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

p-value =

State your conclusion.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs.Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs.    Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs.Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs.

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: H₀: There is no difference in the quality of the training for the programs.
H_a: There is a difference in the quality of the training for the programs. Option C is correct.

Test statistic = 8.39

p - Value = 0.039

Conclusion: Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs. Option D is correct.