Question

In: Statistics and Probability

Suppose the following data show the percentage of 17- to 24-year-olds who are attending college in...

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: μNμMμSμW
Ha: μN = μM = μS = μWH0: μN = μM = μS = μW
Ha: μNμMμSμW     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.

Solutions

Expert Solution

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.   


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