A particular cell phone case is available in a choice of four different colors. A store sells all four colors. To test the hypothesis that sales are equally divided among the four colors, 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 $0.05 ?$
b. What conclusion would be appropriate at significance level $0.01$ 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 $\alpha=0.05$ was used?