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=43.2. You would like to be 90% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?

[Do not round mid-calculation. However, use a critical value rounded to three decimal places — this is important for the system to check answers correctly.]

n =

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin or Error, E = 3, σ = 43.2

The critical value for significance level, α = 0.1 is 1.645.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.645 * 43.2/3)^2
n = 561.12

Therefore, the sample size needed to satisfy the condition n >= 561.12 and it must be an integer number, we conclude that the minimum required sample size is n = 562
Ans : Sample size, n = 562

if you need to rounding decimal then it would be 562 if you dont need nearest integer then it would be 561