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

Given that,

standard deviation = s = 4.8 mph

margin of error = E = 2 mph

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

Sample size = n = [(t _/2,df * s) / E]²

   = [(2.682*4.8) /2 ]²

   = 41.4324

Sample size = 41.4324