You plan to take a random sample from a population of 500 items and build a 95% confidence interval estimate of the population mean.You want a margin of error no bigger than plus/minus 5.You estimate the population standard deviation to be 100.How large a sample is needed?
A)1537
B)452
C)1622
D)377
E)1703

Question

Quizplus · Accepted Answer

To find the sample size (n), use the formula for margin of error (E) in a confidence interval: E = Z * (σ/√n). For a 95% confidence level, Z is approximately 1.96. Rearrange the formula to solve for n: n = (Z * σ / E)^2. Plug in the values: n = (1.96 * 100 / 5)^2 = 1536.64. Since the population is finite (500), use the finite population correction: n' = n / (1 + (n - 1)/N), where N is the population size. n' = 1536.64 / (1 + (1536.64 - 1)/500) ≈ 377.

You Plan to Take a Random Sample from a Population