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 28.2 35.9 59.1 16.4 39.4 32.8 37.9 34.1 32.7 23.1 28.0 23.1 46.5 43.9 41.6 11.9 32.5 32.5 34.0 44.2 14.1 57.7 19.5 27.3 36.2 30.7 30.6 56.9 36.9 64.4 66.8 14.3 38.3 27.6 32.7 36.8 57.6 56.3 30.4 28.7 60.7 78.3 38.3 17.9 42.0 29.5 32.5 75.5 30.3 52.8 35.7 22.9 51.0 28.9 34.5 25.9 60.4 24.3 29.2 58.3 54.6 27.4 21.8 30.5 31.0 28.3 42.4 23.2 25.5 70.7 34.9 74.2 22.0 32.9 37.1 30.1 37.4 29.0 30.3 34.0 26.6 21.2 29.5 32.4 31.7 22.0 56.6 38.5 28.4 39.7 34.1 36.0 39.2 21.8 39.0 35.2 26.8 32.6 Use ? = 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: μN = μM = μS = μW Ha: Not all the population means are equal. H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: μN ≠ μM ≠ μS ≠ μW Ha: μN = μM = μS = μW H0: μN = μM = μS = μW Ha: μN ≠ μM ≠ μS ≠ μW H0: Not all the population means are equal. Ha: μN = μM = μS = μW 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. (A) 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. (B) 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. (C) 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. (D) 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.
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 |
|---|---|---|---|
| 28.2 | 35.9 | 59.1 | 16.4 |
| 39.4 | 32.8 | 37.9 | 34.1 |
| 32.7 | 23.1 | 28.0 | 23.1 |
| 46.5 | 43.9 | 41.6 | 11.9 |
| 32.5 | 32.5 | 34.0 | 44.2 |
| 14.1 | 57.7 | 19.5 | 27.3 |
| 36.2 | 30.7 | 30.6 | 56.9 |
| 36.9 | 64.4 | 66.8 | 14.3 |
| 38.3 | 27.6 | 32.7 | 36.8 |
| 57.6 | 56.3 | 30.4 | 28.7 |
| 60.7 | 78.3 | 38.3 | 17.9 |
| 42.0 | 29.5 | 32.5 | |
| 75.5 | 30.3 | 52.8 | |
| 35.7 | 22.9 | 51.0 | |
| 28.9 | 34.5 | 25.9 | |
| 60.4 | 24.3 | 29.2 | |
| 58.3 | 54.6 | 27.4 | |
| 21.8 | 30.5 | 31.0 | |
| 28.3 | 42.4 | 23.2 | |
| 25.5 | 70.7 | 34.9 | |
| 74.2 | 22.0 | 32.9 | |
| 37.1 | 30.1 | 37.4 | |
| 29.0 | 30.3 | 34.0 | |
| 26.6 | 21.2 | 29.5 | |
| 32.4 | 31.7 | 22.0 | |
| 56.6 | 38.5 | ||
| 28.4 | 39.7 | ||
| 34.1 | 36.0 | ||
| 39.2 | 21.8 | ||
| 39.0 | 35.2 | ||
| 26.8 | |||
| 32.6 |
Use ? = 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: μN = μM = μS = μW
Ha: Not all the population means are equal.
H0: At least two of the population means are equal.
Ha: At least two of the population means are different.
H0: μN ≠ μM ≠ μS ≠ μW
Ha: μN = μM = μS = μW
H0: μN = μM = μS = μW
Ha: μN ≠ μM ≠ μS ≠ μW
H0: Not all the population means are equal.
Ha: μN = μM = μS = μW
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.
(A) 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.
(B) 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.
(C) 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.
(D) 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.
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