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 3 points with 99 % confidence assuming s equals 10.1 based on earlier​ studies? Suppose the doctor would be content with 95 % confidence. How does the decrease in confidence affect the sample size​ required? LOADING... Click the icon to view a partial table of critical values. A​ 99% confidence level requires nothing subjects. ​(Round up to the nearest​ subject.)

Answer 1

solution:-

given that s = 10.1

margin of error E = 3

A​ 99% confidence level requires

99% confidence for Z is 2.58

formula for sample size

=> n = (Z * s/E)^2

n = (2.58 * 10.1/3)^2

n = 75

A​ 95% confidence level requires

95% confidence for Z is 1.96

formula for sample size

=> n = (Z * s/E)^2

n = (1.96 * 10.1/3)^2

n = 44

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

=> Decreasing the confidence level decreases the sample size needed.