Question

An IQ test is designed so that the mean is 100 and the standard deviation is 12 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90​% confidence that the sample mean is within 3 IQ points of the true mean. Assume that sigmaequals12 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin or Error, E = 3, σ = 12

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 * 12/3)^2
n = 43.03

Therefore, the sample size needed to satisfy the condition n >= 43.03 and it must be an integer number, we conclude that the minimum required sample size is n = 44
Ans : Sample size, n = 44