Question

The Highway Safety Department wants to study the driving habits of individuals. A sample of 41 cars traveling on the highway revealed an average speed of 60 miles per hour and a standard deviation of 7 miles per hour. The population of car speeds is approximately normally distributed. Determine a 90% confidence interval estimate for the speed of all cars.

Answer 1

58,21 ≤ μ ≤ 61,79

Explanation:

Normal Distribution

Poputation size n = 41

Population mean X = 60

Population standard deviation σ = 7

Question is: Confidence Interval 90 % ??

As Confidence Interval is 90 % then α = 10 %

And as we are dealing with a two tail test

α/2 = 0,05

We look in Z table for values for α/2 = 0,05 and find

z(α/2) = - 1,64 and z(α/2) = 1,64

Then

Confidence Interval is

X - Zα/2 * σ/√n ≤ μ ≤ X + Zα/2 * σ/√n

60 - ( 1,64 ) * 7/√41 ≤ μ ≤ 60 + ( 1,64 ) * 7/√41

60 - 1,64 * 1,09375 ≤ μ ≤ 60 + 1,64 * 1,09375

60 - 1,79375 ≤ μ ≤ 60 + 1,79375

58,21 ≤ μ ≤ 61,79