Question

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, μ, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate μ. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 3minutes of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 3, σ = 27

The critical value for significance level, α = 0.05 is 1.96.

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 = (1.96 * 27/3)^2
n = 311.17

Therefore, the sample size needed to satisfy the condition n >= 311.17 and it must be an integer number, we conclude that the minimum required sample size is n = 312
Ans : Sample size, n = 312 or 311