Question

Compute the required sample size given the required confidence in the sample results is 99.74%. The level of allowable sampling error is 5% and the estimated population standard deviation is unknown.

Answer 1

it is given that the population standard deviation is unknown, So we will use proportion to calculate the sample size

z score corresponding to 99.74% confidence level is 3.01 using the z distribution table

sampling error or margin of error = ME = 5% or 5/100 = 0.05

We will use the following formula

sample size n = ..............(this formula is used when proportion is not mentioned in the question)

setting the given values, we get

sample size n =

So, the required sample size is 906 (rounded to nearest integer)