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 sigma equals 12.7 question mark Suppose the doctor would be content with 95 % confidence. How does the decrease in confidence affect the sample size​ required?

99% and 95%

Answer 1

At 99% confidence interval the critical value is z_0.005 = 2.58

Margin of error = 4

Or, z_0.005 * = 4

Or, 2.58 * 12.7/ = 4

Or, n = (2.58 * 12.7/4)^2

Or, n = 68

At 95% confidence interval the critical value is z_0.025 = 1.96

Margin of error = 4

Or, z_0.025 * = 4

Or, 1.96 * 12.7/ = 4

Or, n = (1.96 * 12.7/4)^2

Or, n = 39

Since the confidence level decreases, the required of sample size also drcreases.