Question

A superintendent of schools wants to estimate the average work week of teachers in his district. He wants to be 94% sure that the estimate is off by at most 0.8 hours. It is expected that the number of hours will vary with a standard deviation of 3.4 hours. How many teachers should he sample?

Answer 1

The following information is provided,
Significance Level, α = 0.06, Margin or Error, E = 0.8, σ = 3.4

The critical value for significance level, α = 0.061 is 1.88.

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 = (1.88 * 3.4/0.8)^2
n = 63.84

Therefore, the sample size needed to satisfy the condition n >= 63.84 and it must be an integer number, we conclude that the minimum required sample size is n = 64
Ans : Sample size, n = 64