Question

You may need to use the appropriate technology to answer this question.

Three admission test preparation programs are being evaluated. Suppose the scores obtained by a sample of 20 people who used the programs provided the following data.

Program
A	B	C
530	450	600
400	530	640
470	400	590
540	420	470
470	490	570
620	360	610
	550	560

Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use α = 0.05.

State the null and alternative hypotheses.

H₀: Median_A ≠ Median_B ≠ Median_C
H_a: Median_A = Median_B = Median_C

H₀: Median_A = Median_B = Median_C
H_a: Median_A > Median_B < Median_C     

H₀: All populations of test scores are identical.
H_a: Not all populations of test scores are identical.

H₀: Not all populations of test scores are identical.
H_a: All populations of test scores are identical.

H₀: Median_A = Median_B = Median_C
H_a: Median_A ≠ Median_B ≠ Median_C

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.

Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the three test preparation programs.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the three test preparation programs.     

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among the three test preparation programs.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the three test preparation programs.

Answer 1

The statistical software output for this problem is:

Kruskal-Wallis results: Data stored in separate columns Results adjusted for ties DF Chi-Square P-value 2 8.0512876 0.0179 Summary statistics Column. n. Median. Ave. Rank 500 9.6666667 450 6.4285714 590 15.285714

Hence,

Hypotheses:

H₀: All populations of test scores are identical.
H_a: Not all populations of test scores are identical.

Test statistic = 8.05

p - Value = 0.018

Conclusion: Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the three test preparation programs. Option A is correct.