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 3 points with 99 % confidence assuming sigma equals 13.5 question mark Suppose the doctor would be content with 95 % confidence. How does the decrease in confidence affect the sample size​ required? A​ 99% confidence level requires nothing subjects. ​(Round up to the nearest whole number as​ needed.) A 95 % confidence level requires nothing subjects. ​(Round up to the nearest whole number as​ needed.) How does the decrease in confidence affect the sample size​ required? A. The lower the confidence level the smaller the sample size. B. The lower the confidence level the larger the sample size. C. The sample size is the same for all levels of confidence

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 3, σ = 13.5

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 13.5/3)^2
n = 77.79

sample size for 95% CI is 78

The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (2.58 * 13.5/3)^2
n = 134.79

for 99% CI, sample size = 135

The lower the confidence level the smaller the sample size.