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	37.5	60.2	16.3
40.0	33.1	37.9	33.7
32.3	23.0	28.4	22.1
47.0	43.5	41.9	13.2
33.1	32.3	34.0	43.4
15.2	57.6	18.3	26.1
37.2	31.1	30.3	57.0
36.6	64.6	67.6	14.3
38.2	26.9	31.9	36.8
58.1	54.7	29.6	28.9
61.3	78.3	38.4	17.4
	42.2	29.8	31.5
	75.2	30.4	52.2
	36.8	23.3	52.0
	28.4	34.8	25.0
	60.1	24.6	29.8
	57.7	54.9	28.4
	20.3	31.7	31.9
	29.2	42.6	22.1
	25.1	70.4	34.0
	74.6	22.5	33.8
	36.9	29.9	37.6
	28.2	31.4	33.0
	27.3	21.7	28.7
	31.3	31.7	21.8
	57.0	39.0
	27.7	39.8
	32.7	34.7
	39.8	21.4
	39.7	34.9
		26.6
		33.3

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

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.

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.

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.

Answer 1

The statistical software output for this problem is:

Analysis of Variance results: Data stored in separate columns. Column statistics Column: n. Mean Std. Dev. Northeast 11 38.872727 13.003314 Midwest 30 41.76 16.691534 South 32 35.246875 12.494385 West 25 30.84 11.444977 Std. Error 3.9206468 3.0474432 2.2087162 2.2889954 ANOVA table Source DF SS MS F-Stat P-value Columns 3 1743.0425 581.01417 3.0763008 0.0314 Error 94 17753.574 188.8678 Total 97 19496.616

Hence,

Hypotheses:

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

Test statistic = 3.08

P - value = 0.031

Conclusion: Option B is correct.