Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=58.2σ=58.2. You would like to be 95% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?

Use a z* value accurate to TWO places for this problem. (Not z = 2)

Answer 1

A 100(1-)% CI for population mean is expressed as:

where, = Sample mean, = Standard deviation n = Sample size and the term is nothing but the Margin of Error.(E)

Substituting the given values,

  

From standard normal table,

= 3253.105

Hence, the sample size required to be 95% confident that our estimate is within 2 of the true population mean, with  population standard deviation approximately σ=58.2, is estimated to be at least 3253.