In a chi-squared test of a contingency table, the value of the test statistic was $\chi ^ { 2 } = 12.678$ , the significance level was $\alpha$ = 0.05 and the degrees of freedom was 6. Thus:
A) we fail to reject the null hypothesis at $\alpha$ = 0.05.
B) we reject the null hypothesis at $\alpha$ = 0.05.
C) we don't have enough evidence to accept or reject the null hypothesis at $\alpha$= 0.05.
D) we should increase the level of significance in order to reject the null hypothesis.

Question

Quizplus · Accepted Answer

We compare the value of the test statistic (12.678) with the critical value from the chi-squared distribution table at a significance level of 0.05 and 6 degrees of freedom. The critical value is 12.592. Since the test statistic is greater than the critical value, we reject the null hypothesis. Therefore, Choice B is the correct answer.

In a Chi-Squared Test of a Contingency Table, the Value χ2=12.678\chi ^ { 2 } = 12.678χ2=12.678

In a Chi-Squared Test of a Contingency Table, the Value $\chi ^ { 2 } = 12.678$