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A biotechnology firm is planning its investment strategy for future products and research labs

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A biotechnology firm is planning its investment strategy for future products and research labs. A poll found that 5% of a random sample of 1019 adults approved of attempts to clone a human.

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.
b. Explain what that margin of error means.
c. If we only need to be 90% confident, will the margin of error be larger or smaller?
d. Find the margin of error.

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

Mercy

Mercy Added an answer on Jan 13,2021

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tutor

tutor Added an answer on Jul 20,2019

The 99% confidence interval. ,

Margin of error = Z_alpha * sqrt(0.05 * (1-0.05)/1019)

99 percent confidence interval for z score using Excel, =NORM.S.INV(1-0.01/2) = 2.58, and,

The margin of error = 2.58*sqrt(0.05 * (1-0.05)/1019) = 0.018

Meaning of the margin of error:-

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%.

How about the margin of error when a 90% confidence interval is considered.

A 90% confidence interval requires a smaller margin of error. Upper A narrower interval leads to decreased confidence.

Calculation of the margin of error using Excel;

=NORM.S.INV(1-0.01/2) * sqrt(0.05 * (1-0.05)/1019) = 0.011

Then, how does a sample size affect the confidence interval? Smaller samples produce larger margins of error. because the numerator under the square root is divided by a smaller number.

A biotechnology firm is planning its investment strategy for future products and research labs

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