The z, t, and F distributions are closely linked. In fact, it is possible to use an F distribution in all cas es in which a t or a z could be used.

a. If you calculated an F statistic of 4.22 but you could have used a t statistic (i.e., the situation met all criteria for using a t statistic), what would the t statistic have been? Explain your answer. 

b. If you calculated an F statistic of 4.22 but you could have used a z statistic, what would the z statistic have been? Explain your answer. 

c. If you calculated a t statistic of 0.67 but you could have used a z statistic, what would the z statistic have been? Explain your answer. 

d. Cite two reasons that all three types of distributions (i.e., z, t, and F ) are still in use when we really only need an F distribution.