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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?

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. 

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