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: μN =
μM = μS =
μW
Ha: Not all the population means are
equal.H0: μN =
μM = μS =
μW
Ha: μN ≠
μM ≠ μS ≠
μW 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 =
μWH0: 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.
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.
The statistic software output for this problem is:
H0: At least two of the population means are
equal.
Ha: 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.
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