Question

A population has a known standard deviation of 1.27, and the sample space contains 85 values. Find the margin of error needed to create a 99% confidence interval estimate of the mean of the population.

The correct answer is 0.3547 but I don't know why I need a step by step explanation please! I want to understand it better

Answer 1

Standard error=1.27/√85=0.13775.

The critical value for 99% confidence level (2-tailed) is about 2.575 so the margin of error is 2.575×0.13775= 0.3547 aprox.

I used ɑ=1-0.99=0.01 then ɑ/2=0.005 to find the Z value corresponding to 1-0.005=0.9950, which is Z=2.575. That is 2.575 standard deviations from the mean.