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 is correct.

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This is true. In a chi-square goodness of fit test, the null hypothesis assumes that the observed frequencies match the expected frequencies based on the specified probabilities. If the difference between the observed and expected frequencies is small, then the calculated chi-square statistic will be small, which in turn will result in a higher probability of accepting the null hypothesis. Conversely, if the difference is large, the calculated chi-square statistic will be large, which suggests that the null hypothesis is not supported by the data.

In Performing a Chi-Square Goodness of Fit Test with Multinomial