Question

Directions: Show your work to ensure full credit. 1. A simple random sample of 32 cars has a mean braking distance of 137 ft. Assume that braking distances of all cars have a standard deviation of 7 ft. Construct a 95% confidence interval estimate of the mean braking distance of all cars. Interpret your result

Answer 1

Solution :

Given that,

Z$\alpha$/2 = Z_0.025 = 1.96

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

= 1.96 * ( 7 /  $\sqrt$32 )

= 2.43

At 90% confidence interval estimate of the population mean is,

  ± E   

= 137 ± 2.43

= ( 134.57, 139.43 )

We are 95% confident that the true mean of breaking distance of all cars between 134.57 ft. and 139.43 ft.