Chapter 12: Q. 15 (page 802)

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 that the interval ( $51 %, 57 %$ ) contains the true percent 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 $95 %$ of the time.
(c) If Harris takes another poll using the same method, the results of the second poll will lie between $51 %$ and $57 %$ .
(d) Harris should have surveyed more people so that the margin of error would be $0 %$ instead of $3 %$ .
(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

Expert verified

(b) The poll used a method that provides an estimate within $3 %$ of the truth about the population $95 %$ of the time.

Step by step solution

Given information.

We have been given that,

$54 %$ American don't think human beings are developed from earlier species.

Poll's margin of error for $95 %$ confidence = $3 %$ .

We need to find the correct method for estimation of the Poll.

Simplify.

$54 %$ estimate says that American don't think human beings are developed from earlier species.

Census is accurate way to analyze this fact instead of poll.

Margin of error calculated by the sample data is $3 %$ , best way to analyze a confidence interval.

(a) In this option it's either a $0 %$ or $100 %$ that the true percent is within the interval (since the true percent does not change).Therefore ,this is not possible.

A confidence interval approach interval says that if this method was used thousands of times, about $95 %$ chance of the intervals will provide an estimate within the truth $3 %$ of the time.

Hence , the correct option is (b).