Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately ?=62.3?=62.3. 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)
n =________________.

Answer 1

n= 3,727.590 = 3,728

Explanation:

Given that,

Population standard deviation, σ=62.3

Margin of error, ME=2

95% confidence interval

The margin of error is defined as: ME= Z0.05/2 × σ/√n

2 = 1.96×62.3/√n

√n = 1.96×62.3

2

√n = 61.054

n = 3,727.590 = 3,728