In a goodness-of-fit test, suppose that the value of the test statistic is 11.89 and the degrees of freedom are 5. At the 5% significance level, what may one conclude about the null hypothesis?
A) It is rejected, and the p-value for the test is smaller than 0.05.
B) It is not rejected, and the p-value for the test is greater than 0.05.
C) It is rejected, and the p-value for the test is greater than 0.05.
D) It is not rejected, and the p-value for the test is smaller than 0.05.

Question

Quizplus · Accepted Answer

In a goodness-of-fit test, when the test statistic is larger than the critical value at the chosen significance level, we reject the null hypothesis. In this case, we do not know the critical value, but we can calculate the p-value for the test. 
With 5 degrees of freedom, the p-value is less than 0.05 when the test statistic is larger than 11.070. Since 11.89 is greater than 11.070, we can conclude that the null hypothesis is rejected at the 5% significance level. Therefore, the correct choice is A.

In a Goodness-Of-Fit Test, Suppose That the Value of the Test