A random group of students was selected from a large student conference to analy

Question

A random group of students was selected from a large student conference to analyze their class in school. Is there enough evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at a = 0.05?
Year in school: freshmen sophomore junior senior # of students: 8 12 14 24
A. There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 < 9.586.
B. There is evidence to reject the claim that students are equally distributed between the four classes because the test value 9.586 > 9.488.
C. There is evidence to reject the claim that the customers' preferences are distributed between the four classes because the test value 9.586 > 9.488.
D. There is not enough evidence to reject the claim that students are equally distributed between the four classes because the test value 9.488 < 9.586. A random group of students was selected from a large student conference to analyze their class in school. Is there enough evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at a = 0.05?
Year in school: freshmen sophomore junior senior # of students: 8 12 14 24
A. There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 < 9.586.
B. There is evidence to reject the claim that students are equally distributed between the four classes because the test value 9.586 > 9.488.
C. There is evidence to reject the claim that the customers' preferences are distributed between the four classes because the test value 9.586 > 9.488.
D. There is not enough evidence to reject the claim that students are equally distributed between the four classes because the test value 9.488 < 9.586. A random group of students was selected from a large student conference to analyze their class in school. Is there enough evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at a = 0.05?
Year in school: freshmen sophomore junior senior # of students: 8 12 14 24
A. There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 < 9.586.
B. There is evidence to reject the claim that students are equally distributed between the four classes because the test value 9.586 > 9.488.
C. There is evidence to reject the claim that the customers' preferences are distributed between the four classes because the test value 9.586 > 9.488.
D. There is not enough evidence to reject the claim that students are equally distributed between the four classes because the test value 9.488 < 9.586.

Explanation / Answer

Correct Answer: Option B. There is evidence to reject the claim that students are equally distributed between the four classes because the test value 9.586 > 9.488.

H0:  the number of students is equally distributed between the four classes

H1:  the number of students is not equally distributed between the four classes

Let the los be alpha = 5%

From the given data,

Where Ei = 58/4=14.5

Test Statistic, X^2: 9.5862
Critical X^2 : 7.814736
P-Value : 0.0224

Here chisquare value > Chisquare critical value, and P-value < alpha 0.05, so we reject H0

Thus we conclude that   the number of students is not equally distributed between the four classes

Observed Expected freq (Oi) freq (Ei) (Oi-Ei)^2/Ei 8 14.5 2.913793103 12 14.5 0.431034483 14 14.5 0.017241379 24 14.5 6.224137931 Total = 58 58 9.586206897

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