Chapter 11: Q. 2 (page 733)

Which hypotheses would be appropriate for performing a chi-square test?
(a) The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their opinion.
(b) The null hypothesis is that the mean number of students who are strongly opposed is the same for each of the four years. The alternative is that the mean is different for at least two of the four years.
(c) The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the four years at this university. The alternative is that the distribution is different for at least two of the four years.
(d) The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent. The alternative is that these variables are dependent.
(e) The null hypothesis is that there is an association between a year in school and opinion about the tuition increase at this university. The alternative hypothesis is that these variables are not associated.

Short Answer

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(c) The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the four years at this university. The alternative is that the distribution is different for at least two of the four years.

Step by step solution

Given Information

Need to find Which hypotheses would be appropriate for performing a chi-square test.

Explanation

We have been given a two-way table for 4 separate random samples, which implies that we will use a chi-square test for homogeneity (we use a chi-square test of association when the two-way table contains data about 1 sample).

The null hypothesis of a two-way table states that the distributions of each value of one of the variables are the same

$H_{0}$ : The distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at this university

The alternative hypothesis states the opposite of the null hypothesis.

$H_{a}$ : The distribution is different for at least 2 of the 4 years