Assume that the results of a yes/no survey question given to a random sample of male and female subjects are summarized in a 2 × 2 two-way table. Use the given values of the test statistic and the significance level to test for
independence between gender and response.
-Given a test statistic of $\chi ^ { 2 } = 3.4$ and a significance level = 0.01, decide whether gender and response are related
Or not related.
A)not related
B)related

Question

Quizplus · Accepted Answer

The chi-square test statistic of 3.4 must be compared to the critical value from the chi-square distribution table at the given significance level of 0.01. For a 2x2 table, the degrees of freedom are (rows - 1) * (columns - 1) = 1. At a significance level of 0.01 and 1 degree of freedom, the critical value is much higher than 3.4 (typically around 6.63 or higher). Since the test statistic does not exceed the critical value, we fail to reject the null hypothesis, suggesting that gender and response are not related.

Assume That the Results of a Yes/no Survey Question Given χ2=3.4\chi ^ { 2 } = 3.4χ2=3.4

Assume That the Results of a Yes/no Survey Question Given $\chi ^ { 2 } = 3.4$