# Difference Between t statistic and z statistic

I am having trouble understanding this multiple choice question.

The reason the t statistic has more variability than the z statistics is that from sample to sample

a. the sample mean becomes smaller and the sample variance becomes larger

b. the sample mean becomes larger and the sample variance becomes smaller

c. neither the sample mean nor the sample variance remains constant

d. both the sample mean and sample variance become larger

I think it is letter C. but need explanation. If it is not C. why would it be any of the others?

Thanks,

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#### Solution Summary

The reason for the t statistic has more variability than the z statistics from sample to sample is discussed in the solution

$2.19