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 $\chi ^ { 2 } = 7.7$ and a significance level = 0.01, decide whether gender and response are related
Or not related.
A)related
B)not related

Question

Quizplus · Accepted Answer

Given a test statistic of $\chi^2 = 7.7$ and a significance level of 0.01, to determine if gender and response are related, we compare the test statistic to the critical value from the chi-square distribution table for the appropriate degrees of freedom (which, for a 2x2 table, is 1) and the given significance level. The critical value for 1 degree of freedom at the 0.01 significance level is approximately 6.635. Since 7.7 is greater than 6.635, we reject the null hypothesis of independence and conclude that gender and response are related.

Assume That the Results of a Yes/no Survey Question Given χ2=7.7\chi ^ { 2 } = 7.7χ2=7.7

Assume That the Results of a Yes/no Survey Question Given $\chi ^ { 2 } = 7.7$