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 $\chi ^ { 2 } = 2.6$ and a significance level = 0.05, decide whether gender and response are related
Or not related.
A)not related
B)related

Question

Quizplus · Accepted Answer

The test statistic $\chi^2 = 2.6$ must be compared to the critical value from the $\chi^2$ distribution table for the given degrees of freedom (df) and significance level (0.05). For a 2x2 table, df = 1. Without the exact critical value provided, we know that the common critical value for df = 1 at a 0.05 significance level is approximately 3.841. Since 2.6 is less than 3.841, we fail to reject the null hypothesis, indicating that there is not enough evidence to conclude that gender and response are related.

Assume That the Results of a Yes/no Survey Question Given χ2=2.6\chi ^ { 2 } = 2.6χ2=2.6

Assume That the Results of a Yes/no Survey Question Given $\chi ^ { 2 } = 2.6$