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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%in95% 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

01

Given information

American adults=54%

The poll鈥檚 margin of error for 95%confidence was3%.

02

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.

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