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 |
---|---|---|---|
29.0 | 36.4 | 59.3 | 16.1 |
40.1 | 34.0 | 37.6 | 34.3 |
31.6 | 22.8 | 28.4 | 22.6 |
45.6 | 44.3 | 40.9 | 12.0 |
32.5 | 32.5 | 33.3 | 43.0 |
15.6 | 57.6 | 18.8 | 26.2 |
36.7 | 30.8 | 30.3 | 57.8 |
35.8 | 64.2 | 68.2 | 13.8 |
38.1 | 28.4 | 31.9 | 37.2 |
58.4 | 55.9 | 30.2 | 28.6 |
60.0 | 78.1 | 39.0 | 17.4 |
43.0 | 29.2 | 32.1 | |
75.0 | 30.0 | 51.8 | |
36.5 | 23.1 | 50.9 | |
28.8 | 33.7 | 25.9 | |
61.0 | 25.3 | 28.9 | |
58.6 | 53.5 | 26.9 | |
20.2 | 30.3 | 31.8 | |
29.6 | 41.2 | 22.9 | |
24.8 | 69.8 | 33.9 | |
74.7 | 23.1 | 33.1 | |
36.2 | 30.5 | 37.6 | |
28.4 | 30.6 | 33.3 | |
27.3 | 22.2 | 29.3 | |
31.1 | 31.1 | 22.0 | |
56.0 | 38.6 | ||
28.0 | 40.5 | ||
33.5 | 35.3 | ||
38.6 | 20.9 | ||
38.4 | 36.0 | ||
26.5 | |||
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: μN ≠ μM ≠ μS ≠ μWH0: Not all the population means are equal.
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: μN = μM = μS = μW
Ha: 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.
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.
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.