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.

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This is true because the chi-square test statistic is a measure of how far the observed frequencies are from the expected frequencies. If the observed frequencies are very close to the expected frequencies, the chi-square test statistic will be small, indicating a higher probability of concluding that the probabilities specified in the null hypothesis are correct. Conversely, if there is a large difference between observed and expected frequencies, the chi-square test statistic will be large, indicating a lower probability of concluding that the probabilities are correct.

In Performing a Chi-Square Goodness-Of-Fit Test with Multinomial Probabilities,the Smaller