Question

Repair time (X) for an oil change at a car dealership has a population mean of 50 min and a population standard deviation of 7 min. Questions A and B must be done using a pencil and paper.

a.) If a random sample of 50 oil changes is selected. Set up a 99% confidence interval estimate for an oil change.

b.) If a random sample of 75 oil changes is selected. Set up a 95% confidence interval estimate for an oil change.

Answer 1

a)

sample mean, xbar = 50
sample standard deviation, σ = 7
sample size, n = 50

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

ME = zc * σ/sqrt(n)
ME = 2.58 * 7/sqrt(50)
ME = 2.55

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (50 - 2.58 * 7/sqrt(50) , 50 + 2.58 * 7/sqrt(50))
CI = (47.4459 , 52.5541)

b)

sample mean, xbar = 50
sample standard deviation, σ = 7
sample size, n = 75

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 7/sqrt(75)
ME = 1.58

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (50 - 1.96 * 7/sqrt(75) , 50 + 1.96 * 7/sqrt(75))
CI = (48.4158 , 51.5842)