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 Do not 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

To determine whether to reject the null hypothesis, we compare the calculated chi-squared value to the critical value from the chi-squared distribution table at the given degrees of freedom (6) and significance level (0.05). The critical value for 6 degrees of freedom at a 0.05 significance level is approximately 12.592. Since the calculated chi-squared value of 12.678 is greater than the critical value, we reject the null hypothesis at the 0.05 significance level.

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 $\chi ^ { 2 } = 12.678$