Question

# You wish to estimate the population mean amount of time in hours it takes to repair...

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?

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

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