Question

The Highway Safety Department wants to study the driving habits of individuals. A sample of 49 cars traveling on a particular stretch of highway revealed an average speed of 69.7 miles per hour with a standard deviation of 4.8 miles per hour. Round to 4 decimal places.

1. What sample size is needed to estimate the true average speed to within 2 mph at 99% confidence? Note: For consistency's sake, round your t* value to 3 decimal places before calculating the necessary sample size. Choose n =

Answer 1

Solution :

Given that,

= 69.7

s = 4.8

n = 49

Degrees of freedom = df = n - 1 = 49 - 1 = 48

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,48 = 2.682

Margin of error = E = t_/2,df * (s /n)

n =   t_/2,df * s / E

= 2.682 * 4.8 / 2

= 6.4368

n = 6.4368

n = 41.4324