Find the sample size needed to give, with 95% confidence, a margin of error within ±3, if the estimated standard deviation is σ̃ = 100. If the estimated standard deviation is σ̃ = 50. If the estimated standard deviation is σ̃ = 10. Comment on how the variability in the population influences the sample size needed to reach a desired level of accuracy.

We examine the effect of different inputs on determining the sample size needed.