Question

One reason for using a t distribution instead of the standard Normal distribution 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. $z$ requires that the sample size is less than $10\%$ of the population size.

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

Short answer

Option (b) is correct.

Step-by-step solution

Given Information

We are given 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. $z$ requires that the sample size is less than $10\%$ of the population size.

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

Explanation

To calculate confidence interval of population mean, $z$distribution is used. This is used if standard deviation is known.

If standard deviation is known, $t$distribution is used to find critical value.

Option (b) is correct.