Question

The Highway Safety Department wants to study the driving habits of individuals. A sample of 33 cars traveling on a particular stretch of highway revealed an average speed of 68.2 miles per hour with a standard deviation of 9.2 miles per hour. Round to 4 decimal places.

2. What sample size is needed to estimate the true average speed to within 2.5 mph at 95% 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,

Point estimate = sample mean = = 68.2

sample standard deviation = s = 9.2

sample size = n = 33

Degrees of freedom = df = n - 1 = 33 - 1 = 32

1) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 = 0.05

/2 = 0.025

t/2,df = t_0.025,32 = 2.037

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

= 2.037 * (9.2 / 33)

Margin of error = E = 0.0593

The 95% confidence interval estimate of the population mean is,

  ± E  

= 68.2 ± 0.0593

= ( 68.1407, 68.2593)

2) margin of error = E = 2.5

sample size = n = [t/2,df* s / E]²

n = [2.037 * 9.2 / 2.5 ]²

n = 56.19

Sample size = n = 57