Question

When the population standard deviation is unknown:

A)There will be a large amount of sampling error.

B)The resulting margin of error for a confidence interval estimate will tend to be fairly small.

C)The critical value will be negative.

D)The t-distribution must be used to obtain the critical value.

Answer 1

(A) Incorrect, There will be no sampling error because we know that when population standard deviation is unknown, then we use sample standard deviation which is always smaller than population standard deviation. Sample standard deviation does not provide too much sampling error

(B) Incorrect, because margin of error depends on other factors too, which include critical value and sample size. So, we cant say that the margin of error will be small.

(C) Incorrect, critical value has nothing to do with the population standard deviation. So, critical value can be negative or positive.

(D) Correct, because we know that when population standard deviation is unknown, then we always use t distribution and t distribution includes t critical value