Question

1. Assume that the speeds of cars travelling on a stretch of highway are normally distributed. A sample of 25 cars on this highway found a mean speed of 70 mph with a standard deviation of 6 mph.
   1. Construct a 95% confidence interval for the true mean speed of all cars travelling on this stretch of highway. (need check the assumptions)
   2. What is the margin of error in (1).
   3. Interpret the 95% confidence interval in the context of the problem.

Answer 1

Solution :

Given that,

= 70

s =6

n =25

Degrees of freedom = df = n - 1 =25 - 1 = 24

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,24 =2.064 ( using student t table)

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

= 2.064* (6 / 25)

= 2.4768

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

- E < < + E

70 -2.4768 < < 70+ 2.4768

67.5232 < < 72.4768

The 95% confidence interval estimate of the population mean is, ( 67.5232, 72.4768 )