Question

You wish to estimate the population mean amount of time in hours it takes to repair a device. You want to be 90% confident that the sample mean is within 1.25 hours of the population mean. Assume that the population standard deviation 4.7 hours. What is the minimum sample size needed?

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin or Error, E = 1.25, σ = 4.7

The critical value for significance level, α = 0.1 is 1.64.

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 = (1.64 * 4.7/1.25)^2
n = 38.02

Therefore, the sample size needed to satisfy the condition n >= 38.02 and it must be an integer number, we conclude that the minimum required sample size is n = 39
Ans : Sample size, n = 39 or 38