Question

Acidity (pH) of rain follows a normal distribution with a standard deviation of 3. In order to estimate the unknown population mean μ to within one unit with a confidence level of 98%, what would be the required sample size?

Select one:

a. 99

b. 65

c. 55

d. 49

e. 73

Answer 1

The following information is provided,
Significance Level, α = 0.02, Margin or Error, E = 1, σ = 3

The critical value for significance level, α = 0.02 is 2.33.

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 = (2.33 * 3/1)^2
n = 48.86

Therefore, the sample size needed to satisfy the condition n >= 48.86 and it must be an integer number, we conclude that the minimum required sample size is n = 49
Ans : Sample size, n = 49