In: Statistics and Probability
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 |
---|---|---|---|
28.7 | 36.0 | 60.0 | 16.0 |
40.2 | 34.0 | 36.4 | 34.1 |
32.0 | 22.3 | 27.9 | 22.7 |
45.8 | 43.5 | 41.5 | 12.0 |
32.6 | 32.4 | 34.4 | 43.4 |
15.1 | 57.6 | 19.2 | 26.6 |
36.7 | 31.5 | 30.9 | 58.0 |
36.2 | 64.4 | 67.4 | 14.2 |
38.2 | 27.4 | 32.7 | 36.3 |
57.9 | 56.2 | 29.2 | 28.6 |
60.5 | 79.4 | 39.9 | 16.8 |
43.0 | 29.3 | 33.1 | |
75.3 | 30.2 | 52.2 | |
36.7 | 23.3 | 51.7 | |
28.7 | 33.2 | 25.1 | |
60.4 | 25.3 | 29.6 | |
57.7 | 53.8 | 27.0 | |
21.4 | 30.2 | 30.9 | |
28.7 | 41.1 | 22.4 | |
25.1 | 71.0 | 34.1 | |
74.6 | 22.9 | 32.8 | |
36.0 | 30.0 | 36.5 | |
28.1 | 31.2 | 33.5 | |
27.4 | 21.3 | 28.3 | |
32.0 | 31.0 | 22.5 | |
57.6 | 37.7 | ||
28.3 | 41.0 | ||
33.1 | 35.3 | ||
39.9 | 21.0 | ||
39.4 | 35.5 | ||
26.0 | |||
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: μN ≠
μM ≠ μS ≠
μW
Ha: μN =
μM = μS =
μWH0:
μN = μM =
μS = μW
Ha: μN ≠
μM ≠ μS ≠
μW H0:
Not all the population means are equal.
Ha: μN =
μM = μS =
μWH0:
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.
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 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 statistical software output for this problem is :
H0: μN =
μM = μS =
μW
Ha: Not all the population means are equal.
Test statistics = 3.21
P-value = 0.027
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.