Question

A Harris poll found that $54\%$of American adults don’t think that human beings developed from earlier species. The poll’s margin of error for $95\%$confidence was $3\%$. This means that

a. there is a $95\%$chance the interval ($51\%,57\%$) contains the true per cent of American adults who do not think that human beings developed from earlier species.

b. the poll used a method that provides an estimate within 3% of the truth about the population in $95\%$of samples.

c. if Harris conducts another poll using the same method, the results of the second poll will lie between $51\%$and $57\%$

d. there is a 3% chance that the interval is incorrect.

e. the poll used a method that would result in an interval that contains $54\%$in$95\%$ of all possible samples of the same size from this population.

Short answer

The correct option is (b) the poll used a method that provides an estimate within $3\%$of the truth about the population in $95\%$of samples.

Step-by-step solution

Given information

American adults$=54\%$

The poll’s margin of error for $95\%$confidence was$3\%$.

Explanation

It is assumed that the point estimate in the poll based on the sample is $54\%$. Unless a census was performed, which is difficult to accomplish with a poll, this is not the genuine population proportion.

Only one of the responses is the correct technique to examine a confidence interval, and $3\%$is the margin of error calculated by the sample data.

Because it's either a $0\%$or a $100\%$, it's not (a) possible that the true percent is within the interval because the true per cent does not vary.

As a result of the confidence interval strategy, roughly $95\%$of the intervals will yield an estimate within the truth $3\%$of the time if this method is applied thousands of times.

As a result, choice (b) is the correct answer, indicating that the poll utilised a method that, $95\%$of the time, offers an estimate within $3\%$of the truth regarding the population.