Question

You design a study aimed at estimating the population average commuting time based on a large sample of students. Assume that a commute time for a randomly selected student is distributed normally, with the population standard deviation of 12 minutes.

1. What is the smallest sample size needed to estimate the population average with 99% confidence so that the margin of error will not exceed 5 minutes? Critical Value =

   Sample Size =

2. If we want to estimate the population average commute time (using the 95% confidence level) within the bound of ± 3 minutes, what is the smallest sample size?
   Sample Size =

   Critical Value =

3. What will be the width of the 90% confidence interval if a sample of size 100 is selected?

   Width = Critical Value =

Answer 1

Here it is given that standard deviation is 12

1. For 99% CI, z value is 2.58 as P(-2.58<z<2.58)=0.99, E=5

So we will find n using formula of E

So

2. For 95% CI, z value is 1.96 as P(-1.96<z<1.96)=0.95

and E=3

So

3. For 90% CI, z value is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of Error is