Question

A research scholar wants to know how many times per hour a certain strand of virus reproduces. He wants to construct the 95% confidence interval with a maximum error of 0.22 reproductions per hour. Assuming that the mean is 9.7 reproductions and the standard deviation is known to be 2.4 , what is the minimum sample size required for the estimate? Round your answer up to the next integer.

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 0.22, σ = 2.4

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 * 2.4/0.22)^2
n = 457.18

Therefore, the sample size needed to satisfy the condition n >= 457.18 and it must be an integer number, we conclude that the minimum required sample size is n = 458
Ans : Sample size, n = 458