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The z t and f distributions are closely linked in fact it


Question: The z, t, and F distributions are closely linked. In fact, it is possible to use an F distribution in all cases 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.

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Basic Statistics: The z t and f distributions are closely linked in fact it
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When the sample size is small and the population standard deviation is unknown, then we need to use small sample test, called t test to test the claim. on the other hand, if the sample size is small and known population standard deviation or if the sample size is large enough, then we can proceed with larger sample test called z test to test the claim.

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