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
28.6	36.2	60.5	16.2
39.1	32.7	37.1	33.2
31.1	22.9	28.0	21.5
46.0	44.1	40.5	12.1
33.0	31.5	34.4	43.8
14.7	59.1	18.3	27.0
37.1	31.3	30.9	57.1
36.9	64.6	67.8	14.5
37.5	26.8	33.3	36.8
58.6	55.6	30.2	28.4
60.7	78.0	38.4	16.8
	42.5	29.9	32.8
	74.6	29.5	52.0
	36.5	23.8	52.2
	29.5	33.5	25.9
	60.5	24.1	30.4
	57.7	53.8	28.4
	20.2	30.6	31.6
	29.1	41.2	23.4
	24.7	70.2	34.3
	74.0	23.4	32.9
	36.4	31.0	36.3
	28.7	30.7	33.7
	27.2	22.3	28.2
	32.3	31.2	21.6
	56.8	37.7
	28.6	40.9
	33.8	34.9
	38.7	21.6
	39.6	35.8
		26.9
		32.4

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: 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    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_WH₀: Not all the population means are equal.
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.

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 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.    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.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.

Answer 1

The statistic software output for this problem is:

Analysis of Variance results: Data stored in separate columns. Column statistics Column . n Mean Std. Dev. Northeast 11 38.481818 13.070717 Midwest 30 41.806667 16.645594 South 32 35.15 12.358985 West 25 30.844 11.505581 Std. Error 3.9409694 3.0390559 2.1847806 2.3011163 ANOVA table Source DF SS MS F-Stat Columns 3 1745.9711 581.99037 3.0985345 Error 94 17655.797 187.82762 Total 97 19401.768 P-value 0.0305

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

Test statistics = 3.10

P-value = 0.031

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.