A particular paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally divided among the four choices, a random sample of 100 purchases is identified.
a. If the resulting $X^{2}$ value were $6.4$, what conclusion would you reach when using a test with significance level .05?
b. What conclusion would be appropriate at significance level. $.01$ if $X^{2}=15.3 ?$
c. If there were six different covers rather than just four. what would you conclude if $X^{2}=13.7$ and a test with $\alpha=.05$ was used?