Chapter 8.3, Problem 75E

To determine

The correct statement for the calculation of the confidence interval that (a) z can be used only for the large sample, (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 does not include confidence level at the bottom, (e) a z critical value lead to wider interval the critical value.

Answer to Problem 75E

The correct option is (b).

Explanation of Solution

From a normal populationz can also be used for small sample. Thus, statement(a) is incorrect.

To calculate the confidence interval z requires to know the population standard deviation. Thus,statement (b) is correct.

Instead of a simple random sample only a random sample is sufficient to calculate the confidence interval, thus, statement (c) is incorrect.

The critical value still can be determining from the standard normal table if it the table does not include confidence. Thus, option (d) is incorrect.

A z critical value does not dependent on the width of the interval. Thus, option (e) is incorrect.

Hence, the correct option is(b).