Question

A sample of size π=95 is drawn from a population whose standard deviation is σ=27. 

Part 1 of 2 

(a) Find the margin of error for a 99% confidence interval for H. Round the answer to at least three decimal places. 

The margin of error for a 99% confidence interval for u is _______ . 

Part 2 of 2 

(b) If the confidence level were 90%, would the margin of error be larger or smaller? 

Answer 1

a. z value for 99% CI is 2.576 as P(-2.576

So Margin of Error is $E=z*\frac{\sigma }{\sqrt{n}}=2.576*\frac{27}{\sqrt{95}}=7.136$

b. Instead of 99% if we use 90% CI, z value will decrease and make Margin of Error will be smaller

So answer here is Smaller, because the confidence level is smaller.