Question

1) A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 99%confidence if​

(a) he uses a previous estimate of 25​%?

​(b) he does not use any prior​ estimates?

​(a)n=?

​(Round up to the nearest​ integer.

​(b)n=?

​(Round up to the nearest​ integer.)

2) Determine the point estimate of the population mean and margin of error for the confidence interval.

Lower bound is 20​,upper bound is 26.

The point estimate of the population mean is

The margin of error for the confidence interval is

Answer 1

1)

Given that,

margin of error = E = 0.02

Z_/2 = 2.576

(a)

= 0.25

1 - = 0.75

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (2.576 / 0.02)² * 0.25 * 0.75

= 3111

sample size = n = 3111

(b)

= 0.5

1 - = 0.5

n = (2.576 / 0.02)² * 0.5 * 0.5

= 4148

sample size = n = 4148

2)

Sample mean = = (20 + 26) / 2 = 23

Margin of error = E = Upper confidence interval -   = 26 - 23 = 3