Question

In performing a chi-square goodness-of-fit test with multinomial probabilities, the ___________ the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.

larger

smaller

Answer 1

Smaller

In performing a chi-square goodness-of-fit test with multinomial probabilities, the smaller the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.

Explanation:

For the chi-square goodness of fit test, if the difference between observed and expected frequencies is smaller, then total sum or test statistic will be less and this will increase the probability of do not rejecting the null hypothesis of chi square test for goodness of fit. If the difference is larger, the p-value would be smaller, and this will lead to rejection of the null hypothesis.