In a goodness-of-fit test, suppose that the value of the test statistic is 13.08 and the number of degrees of freedom is 6. At the 5% significance level, the null hypothesis is:
A) rejected and p-value for the test is smaller than 0.05
B) not rejected, and p-value for the test is greater than 0.05
C) rejected, and p-value for the test is greater than 0.05
D) not rejected, and p-value for the test is smaller than 0.05
E) none of these

Question

Quizplus · Accepted Answer

In a goodness-of-fit test, the null hypothesis is that the observed frequency distribution follows the expected theoretical distribution. A small p-value indicates that it is unlikely to get such a good match between the observed and expected values by chance, thus providing evidence to reject the null hypothesis.

In this case, since the test statistic is greater than the critical value (which is 12.592 according to a chi-square distribution table with 6 degrees of freedom and a 5% level of significance), the null hypothesis is rejected. Additionally, since the p-value for the test is smaller than 0.05 (the level of significance), this provides further evidence to reject the null hypothesis. Therefore, the answer is A.

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