Final answer:
If you fail to reject the null hypothesis in a chi-square test for goodness-of-fit, it suggests that the expected and observed frequencies for the cells should be about equal, indicating a good fit to the expected distribution.
Step-by-step explanation:
When conducting a chi-square test for goodness-of-fit, the goal is to compare observed frequencies in each category with the expected frequencies. The null hypothesis posits that observed frequencies come from the same distribution as the expected frequencies. If you fail to reject the null hypothesis, it suggests that there is not sufficient evidence to say that the data does not fit the expected distribution. In this context, if the null hypothesis is not rejected, the answer to the student's question would be that the observed and expected frequencies for the cells should be about equal, implying that the observed data fits the expected distribution well.
Note that this does not necessarily mean the observed frequencies are identical to the expected frequencies, but rather that there is no statistically significant difference between them. The chi-square goodness-of-fit test does not involve comparing variances directly; thus, options (a) and (b) are not relevant to the result of failing to reject the null hypothesis in this test.