Question

A biotechnology firm is planning its investment strategy for future products and research labs. A poll found that

5

​%

of a random sample of

1047

adults approved of attempts to clone a human. Use this information to complete parts a through e.

​a) Find the margin of error for this poll if we want

99

​%

confidence in our estimate of the percent of adults who approve of cloning humans.

MEequals

0.017

​(Round to three decimal places as​ needed.)

​b) Explain what that margin of error means.

A.

The margin of error is the value that should be subtracted from the

99

​%

confidence level to obtain the​ pollsters' true confidence level.

B.

The pollsters are

99

​%

confident that the true proportion of adults who approve of attempts to clone a human is within the margin of error of the estimated

5

​%.

Your answer is correct.

C.

The margin of error is the width of the confidence interval that contains the true proportion of adults who approve of attempts to clone a human.

D.

The pollsters are

99

​%

confident that the margin of error contains the true proportion of adults who approve of attempts to clone a human.

Answer 1

Solution(a)

Proportion = 0.05

No. Of sample = 1047

Margin of error can be calculated as

Margin of error = zalpha/2*sqrt(p*(1-p)/n)

Alpha = 0.01, alpha/2 = 0.005, Zalpja/2 = 2.575

Margin of error = 2.575*sqrt(0.05*0.95/1047) = 2.575*0.0067 = 0.017

Solution(b)

Confidence interval can be calculated as

Point estimate +/- margin of error

So confidence interval is width is double of margin of error.

So its answer is B. I.e. the pollsters are 99% confident that the true proportion of adults who approves of attempts to clone a human is within the margin of error of the estimated 5% .

So its answer is B.