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, 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

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Katrina Lewis · Accepted Answer

Final Answer : A, Explanation :  In a goodness-of-fit test, the test statistic follows a chi-square distribution. With degrees of freedom 5 and a test statistic value of 11.89, we would calculate the corresponding p-value using the chi-square distribution table or a calculator. Since this is a one-tailed test with a significance level of 5%, we compare the p-value to 0.05.If the p-value is less than 0.05, we reject the null hypothesis. If the p-value is greater than 0.05, we fail to reject the null hypothesis.In this case, since the test statistic value is relatively large and we have a small degrees of freedom in chi-square distribution, we can conclude p-value is smaller than 0.05. Hence, we reject the null hypothesis and select choice A.

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