Question

with 99 percent confidence interval assuming alpha = 13.4 suppose the doctor is contend with 95% confidence interval.. how does the decrease in confidence interval affect the sample size required?

a 99% interval require how many subject?
a 95% interval require how many subject?

how does the decrease in confidence interval affect sample size required?
a) the sample size is the same for all levels of confidence
b) the lower the confidence level the larger the sample size
c) the lower the confidence level the smaller the sample size

Answer 1

The min sample size n can be found using this formula

\[\Large n = \left(\frac{z*\sigma}{E}\right)^2\]

now they don't mention the margin of error E or the standard deviation sigma, but that doesn't matter. You can make those values to be whatever you want (whatever you pick, n will either always increase or always decrease)

Answer 2

z is the critical z score based on the confidence level

eg: 95% confidence level ----> z = 1.96

the z value is found using a table like this one

https://www.ltcconline.net/greenl/courses/201/estimation/smallConfLevelTable.htm

Answer 3

whatever you pick for E and sigma, keep those values fixed

also remember to always round the value of n up to the nearest whole number