Question: You are performing a goodness-of-fit test with four categories, all of which are supposed to be equally likely. You have a total of 100 observations.

You are performing a goodness-of-fit test with four categories, all of which are supposed to be equally likely. You have a total of 100 observations. The observed frequencies are 21, 26, 31, and 22, respectively, for the four categories.
a. Show that you would fail to reject the null hypothesis for these data for any reasonable significance level.
b. The sum of the absolute differences (between the expected and the observed frequencies) for these data is 14 (i.e. 4 + 1 + 6 + 3 = 14) Is it possible to have different observed frequencies keeping the sum at 14 so that you get a p-value of .10 or less?

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