Question

The ages of a group of 152 randomly selected adult females have a standard deviation of 18.5 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so leta 18.5 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume Pat we want 90% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? The required sample size is - (Round up to the nearest whole number as needed.)

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin or Error, E = 0.5, σ = 18.5

The critical value for significance level, α = 0.1 is 1.64.

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 = (1.64 * 18.5/0.5)^2
n = 3682.06

Therefore, the sample size needed to satisfy the condition n >= 3682.06 and it must be an integer number, we conclude that the minimum required sample size is n = 3683
Ans : Sample size, n = 3683 or 3682