Question

A doctor wants to estimate the HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 4 points with 99 % confidence assuming σ= 10.1? 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 how many subjects?

Answer 1

z score for 99% confidence level is 2.58 (using z distribution table)

margin of error(ME) = 4

population standard deviation (sd) = 10.1

sample size n = ((z*sd)/ME)^2

= ((2.58*10.1)/4)^2

= 6.5145^2

= 42.44

= 43 (rounded to next integer)

Decrease in confidence level will reduce the sample size because the z critical value will decrease with decrease in confidence level, which will directly reduce the sample size

z score for 90% confidence level is 1.645 (using z distribution table)

margin of error(ME) = 4

population standard deviation (sd) = 10.1

sample size n = ((z*sd)/ME)^2

= ((1.645*10.1)/4)^2

= 17.25

= 18 (rounded to next integer)