Q. AP4.15 A Harris poll found that 54%聽of... [FREE SOLUTION]

魅影直播

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 魅影直播 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 12: Q. AP4.15 (page 829)

A Harris poll found that $54 %$ of American adults don鈥檛 think that human beings developed from earlier species. The poll鈥檚 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

Expert verified

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鈥檚 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.