Question

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s equals s=15.3 based on earlier​ studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size​ required?

A​ 99% confidence level requires ????? subjects.

A 90% confidence level requires ????? subjects. ​

How does the decrease in confidence affect the sample size​ required?

A. The sample size is the same for all levels of confidence

. B. Decreasing the confidence level does not change the sample size needed.

C. Decreasing the confidence level decreases the sample size needed.

D. Decreasing the confidence level increases the sample size needed.

Answer 1

Solution :

Given that,

Population standard deviation = s = 15.3

Margin of error = E = 2

Z_/2 = 2.576

sample size = n = [Z_/2* s / E] ²

n = [2.576 * 15.3 / 2]²

n = 389

Sample size = n = 389

A​ 99% confidence level requires 389 subjects .

Z_/2 = 1.645

sample size = n = [Z_/2* s / E] ²

n = [2.576 * 15.3 / 2]²

n = 159

Sample size = n = 159

A​ 90% confidence level requires 159 subjects .

C. Decreasing the confidence level decreases the sample size needed.