Chapter 14.3, Problem 14.5E

Suppose that a response can fall into one of $k=5$ categories with probabilities $p_1,p_2,\mathrm{.....},p_5$ 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 chis quare statistic. how many degrees of freedom would the test have?
c. Find the critical value of $x^2$ that defines the rejection region with $\alpha =.05$ .
d. Calculate the observed value of the test statistic.
e. Conduct the test and state your conclusions.