Question

A monthy opinion survey is based on a sample of 1,500 persons, "scientifically chosen as a representative cross section of the American public." The press release warns that the estimates are subject to chance error, but guarantees that they are "reliable to within two percentage points." The word "reliable" is ambiguous. According to statistical theory, the guarantee should be interpreted as follows: (i) In virtually all these surveys, the estimates will be within two percentage points of the parameters. (ii) In most such surveys, the estimates will be within two percentage points of the parameters, but in some definite percentage of the time larger errors are expected. Choose the appropriate interpretation and explain.

Answer 1

(ii) In most such surveys, the estimates will be within two percentage points of the parameters, but in some definite percentage of the time larger errors are expected.

This is because of the confidence level of the margin of error.

Explanation:

These estimates are called confidence interval of proportions.

They have a margin of error that depends of the confidence level.

A confidence level of x% means that we are x% sure on the margin of error.

So the correct interpretation is:

(ii) In most such surveys, the estimates will be within two percentage points of the parameters, but in some definite percentage of the time larger errors are expected.