Conduct the appropriate test of specified probabilities using the information given . Write the null and alternative hypotheses, give the rejection region with a 5.05 and calculate the test statistic. Find the approximate p-value for the test. Conduct the test and state your conclusions.

16. The five categories are equally likely to occur, and the category counts are shown in the table:

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Category 1 2 3 4 UT 5 Observed Count 47 63 74 51 65