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 1017 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 90% confidence in our estimate of the percent of adults who approve of cloning humans.

ME=...... (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 90% confidence level to obtain the pollsters' true confidence level.

B.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.

C.The pollsters are 90% confident that the margin of error contains the true proportion of adults who approve of attempts to clone a human.

D.The pollsters are 90% 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%.

c) If we need to be 95% confident, will the margin of error be larger or smaller?

A. A 95% confidence interval requires a smaller margin of error. Upper A wider interval leads to decreased confidence.

B. A 95% confidence interval requires a larger margin of error. In order to increas confidence comma the interval must be wider.

C. A 95% confidence interval requires a smaller margin of error. Upper A narrower interval leads to decreased confidence.

D. A 95% confidence interval requires a larger margin of error. In order to increase confidence comma the interval must be narrower.

d) Find that margin of error.

ME=...... (Round to three decimal places as needed.)

e) In general, if all other aspects of the situation remain the same, would smaller samples produce smaller or larger margins of error?

A. Smaller samples produce smaller margins of error.

B. Smaller samples produce larger margins of error.

Answer 1

a)

Sample proportion, p = 5% = 0.05

Sample size, n = 1017

Standard error of the sample proportion = = 0.006834179

z value for 90% confidence interval is 1.645

Margin of error = 1.645 * 0.006834179 = 0.011

ME = 0.011

b)

D.The pollsters are 90% 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%.

c)

z value for 95% confidence intercal is 1.96 which is larger than that for 90% confidence interval. The margin of error depends on the z value. Thus, margin of error increases with increase in confidence interval. If the margin of error increases, the width of the interval increases.

B. A 95% confidence interval requires a larger margin of error. In order to increase confidence comma the interval must be wider.

d)

For 95% confidence interval,

ME = 1.96 * 0.006834179 = 0.013

e)

Standard error increases with decrease in sample size (smaller samples). Margin of error increases with increase in standard error. Thus, margin of error increases with decrease in sample size.

B. Smaller samples produce larger margins of error.