Question

Suppose the following data show the percentage of 17- to 24-year-olds who are attending college in several metropolitan statistical areas in four geographic regions of the United States.

Northeast	Midwest	South	West
29.2	36.8	59.4	16.5
40.5	33.9	37.9	32.9
32.1	22.8	27.7	23.0
46.2	43.2	40.9	12.8
32.9	32.8	34.7	44.2
15.4	59.1	18.9	26.2
36.4	30.9	29.8	56.9
36.3	63.8	68.0	13.8
36.9	26.8	32.0	37.7
58.2	56.3	30.5	28.0
60.6	79.1	39.8	17.6
	43.0	29.4	33.1
	73.9	30.2	52.1
	35.8	24.2	51.9
	29.3	33.3	24.7
	60.1	25.3	29.6
	58.5	54.6	26.8
	21.2	31.4	32.0
	28.6	41.5	22.8
	25.5	69.7	35.2
	73.4	23.3	33.0
	37.5	30.5	37.8
	27.8	31.5	33.8
	27.1	22.0	28.8
	32.3	31.8	21.8
	56.9	37.5
	27.6	40.3
	33.7	34.8
	38.9	20.9
	38.5	35.4
		26.5
		32.2

Use α = 0.05 to test whether the mean percentage of 17- to 24-year-olds who are attending college is the same for the four geographic regions.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: μ_N = μ_M = μ_S = μ_W

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.     

H₀: μ_N ≠ μ_M ≠ μ_S ≠ μ_W
H_a: μ_N = μ_M = μ_S = μ_W

H₀: μ_N = μ_M = μ_S = μ_W
H_a: Not all the population means are equal.

H₀: μ_N = μ_M = μ_S = μ_W
H_a: μ_N ≠ μ_M ≠ μ_S ≠ μ_W

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 not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

Do not reject H₀. There is not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.     

Do not reject H₀. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

Reject H₀. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

Answer 1

The statistical software output for this problem is:

Analysis of Variance results: Data stored in separate columns. Column statistics ColumnnMean Std. Dev. Northeast 11 38.609091 12.821424 Midwest 30 41.836667 16.605036 South 32 35.184375 12.302586 West 25 30.92 11.520778 Std. Error 3.8658047 3.031651 2.1748105 2.3041557 ANOVA table Source DF SS M S F-Stat P-value Columns 3 1737.0996 579.03319 3.1071423 0.0302 Error 94 17517.421 186.35554 Total 97 19254.521

Hence,

Hypotheses:

H₀: μ_N = μ_M = μ_S = μ_W
H_a: Not all the population means are equal.

Test statistic = 3.11

p - Value = 0.030

Conclusion:

Reject H₀. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions. Option D is correct.