Question

The Highway Safety Department wants to study the driving habits of individuals. A sample of 32 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. What sample size should be chosen if we want a margin of error of less than 2 miles per hour for a 95% confidence interval?

Answer 1

Solution :

Given that,

Population standard deviation = = 11

Margin of error = E = 2

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 *11 / 2 ]²

n = 116.20

Sample size = n = 117