Question

The owner of an oil change shop would like to know the mean time it takes to do an oil change at the shop. He takes a random sample of 16 cars that are serviced and finds a sample average of 20.5 minutes and a standard deviation of 7.4 minutes

Construct a 90% confidence interval for the true mean time to do an oil change to a car.

a) Lower Bound

b) Upper Bound

Answer 1

bar{x} = 20.5 minutes b = 7.4 minutes = 16 degree of Freedom = n - 1 = 16 - 1 =15 At 90% confidence level the t is, alpha = 1 - 90% alpha = 1 - 0.90 alpha = 0.10 alpha/2 = 0.05 t alpha/2 , df = t 0.05, 15 = 1.753 A 90% confidence interval for the mu is bar{x} pm t alpha/2 , df into 6/ squareroot n 20.5 pm 1.753 into 7.4/ squareroot 16 20.5 pm 3.2 (17.3 , 23.7) a) Lower Bound = 17.3 b) Upper Bound = 23.7