Question

The recorded speeds (in mi/hr) is observed from a sample of 40 cars traveling on the 101 freeway near La Conchita. The sample has a mean of 68.4 mi/hr and a standard deviation of 5.7 mi/hr (based on data from Sigalert). a. Find a 98% confidence interval estimate for the mean speed of all cars. [5 pts] b. Provide an interpretation of your interval in the context of the data. [2pts]

Answer 1

Solution :

a) degrees of freedom = n - 1 = 40 - 1 = 39

t$\alpha$/2,df = t_0.01,39 = 2.426

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.426 * (5.7 / $\sqrt$ 40)

Margin of error = E = 2.19

The 98% confidence interval estimate of the population mean is,

  ± E  

T

= 68.4 ± 2.19

= ( 66.21, 70.59 )

b) We are 98% confident that the true mean speed of all cars between 66.21 mi / hr and 70.59 mi / hr.