Question

state whether each standardized test statistic $chi^2$ allows you to reject the null hypothesis. explain.
(a) $chi^2 = 29.606$ \t\t\t(b) $chi^2 = 0$
(c) $chi^2 = 1.974$ \t\t\t(d) $chi^2 = 31.492$

(a) choose the correct answer below.
\\(\bigcirc\\) a. do not reject the null hypothesis because the standardized test statistic is not in the rejection region.
\\(\bigcirc\\) b. reject the null hypothesis because the standardized test statistic is in the rejection region.
\\(\bigcirc\\) c. reject the null hypothesis because the standardized test statistic is not in the rejection region.
\\(\bigcirc\\) d. do not reject the null hypothesis because the standardized test statistic is in the rejection region.

Explanation:

Step1: Understand Rejection Region

The rejection region for a chi - square test is the area where \(\chi^{2}>\chi_{0}^{2}\) (from the graph, \(\chi_{0}^{2} = 31.4100\)).

Step2: Analyze \(\chi^{2}=29.606\)

Compare \(29.606\) with \(31.4100\). Since \(29.606<31.4100\), the test statistic is not in the rejection region. So we do not reject the null hypothesis.

Answer:

A. Do not reject the null hypothesis because the standardized test statistic is not in the rejection region.