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)

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