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 44 points with 99 %99% confidence assuming sigma equals 17.8 question mark ?=17.8? suppose the doctor would be content with 95 %95% confidence. how does the decrease in confidence affect the sample size? required?

Answer 1

 

Given the following:

Sigma                                 = 17.8

E                                         = 44 points

Confidence interval        = 99% - 2.58

Confidence interval        = 95% - 1.96

In order to get the sample size, use the formula:

For 99% confidence level

n            = [ (z value x s) / E ]2

n            = [ (2.58 x 17.8) / 44]2

n            = 1. 089 or 1 (rounded up)

For 95% confidence level

n            = [ (z value x s) / E ]2

n            = [ (1.96 x 17.8) / 44]2

n            = 0.628 or 1 (rounded up)

As we decrease the confidence level, from 99% to 95%, our confidence interval gets smaller. In additional, to be more confident that our interval actually comprises the population mean we have to increase the size of the interval. To ease that trade off between level of confidence and the precision of our interval is to primarily increase the sample size.