Question

Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that σ is in the neighborhood of 0.5 pH an that you want your estimate to lie within 0.1 of µ with probability near 0.95. Approximately how many rainfalls must be included in your sample (one pH reading per rainfall)?

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 0.1, σ = 0.5

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 * 0.5/0.1)^2
n = 96.04

Therefore, the sample size needed to satisfy the condition n >= 96.04 and it must be an integer number, we conclude that the minimum required sample size is n = 97
Ans : Sample size, n = 97 or 96