In a goodness-of-fit test, suppose that a sample showed that the observed frequency $f _ { i }$ and expected frequency $e _ { i }$ were equal for each cell i. Which of the following best describes the decision for the hypothesis test?
A)Reject Ho at $\alpha$ of 0.05 but do not reject Ho at $\alpha$of 0.025.
B)Reject Ho at any level of $\alpha$.
C)Do not reject Ho at any level of $\alpha$.
D)Do not reject Ho at $\alpha$ of 0.05 but reject Ho at $\alpha$ of 0.025.

Question

Quizplus · Accepted Answer

When the observed frequencies $f_i$ match the expected frequencies $e_i$ for each cell, it indicates a perfect fit between the observed data and the expected distribution under the null hypothesis $H_0$. This scenario would result in a chi-square statistic of 0, leading to a p-value greater than any conventional alpha level ($\alpha$), thus we would not reject $H_0$ at any level of $\alpha$.

In a Goodness-Of-Fit Test, Suppose That a Sample Showed That fif _ { i }fi​

In a Goodness-Of-Fit Test, Suppose That a Sample Showed That $f _ { i }$