Question

A confidence interval can be useless if it is too wide (i.e., the margin of error is too big). Suppose that the population standard deviation is known. Which one of the following recommendations will NOT reduce the width (i.e., the margin of error) of the confidence interval?

a. increase the confidence level for the interval estimation, without changing the sample size.

b. lower the confidence level for the interval estimation, without changing the sample size

c. lower the confidence coefficient for the interval estimation, without changing the sample size

d. increase the sample size, without changing the confidence level

Answer 1

Solution:

Answer is : a. increase the confidence level for the interval estimation, without changing the sample size.

If we increase the confidence level , then the margin of error increases i.e. the width of the interval increases.

Given that ,the population standard deviation is known. In this case we use z distribution to construct the confidence interval for mean.

The margin of error is given by

E =  /2 * ( / n )

As level of confidence increases , the value of   increases and margin of error also increases.

In options b , c and d , the margin of error decreases.