Suppose that a response can fall into one of k 5 categories with probabilities p1, p2, . . . , p5 and that n = 300 responses produced these category counts:

a. Are the five categories equally likely to occur? How would you test this hypothesis?
b. If you were to test this hypothesis using the chi square statistic, how many degrees of freedom would the test have?
c. Find the critical value of x2 that defines the rejection region with α = .05.
d. Calculate the observed value of the test statistic.
e. Conduct the test and state your conclusions.

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Category 1 2 34 Observed Count 47 63 74 51 65