Question

One reason for using a $t$distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

(a) $z$can be used only for large samples.

(b) $z$requires that you know the population standard deviation $\sigma$.

(c) $z$requires that you can regard your data as an SRS from the population.

(d) the standard Normal table doesn't include confidence levels at the bottom.

(e) a $z$critical value will lead to a wider interval than a $t$critical value.

Short answer

(b) $z$ requires that you know the population standard deviation $\sigma$.

Step-by-step solution

Given Information

(a) $z$can be used only for large samples.

(b) $z$requires that you know the population standard deviation $\sigma$.

(c) $z$requires that you can regard your data as an SRS from the population.

(d) the standard Normal table doesn't include confidence levels at the bottom.

(e) a $z$critical value will lead to a wider interval than a $t$critical value.

Explanation

(a) False, $z$can also be used for small samples from a Normal population.

(b) True, if you know the population standard deviation $\sigma$, then you use the $z$-procedure, else you use the $t$-procedure.

(c) False, a random sample instead of a simple random sample is also sufficient.

(d) False, you can still determine the critical value using the standard Normal table.

(e) False, the procedure to be used is not dependent on the width of the interval.