Question

Questions A and B must be done using a pencil and paper.

A.) Assume that a sample of 16 tires is randomly chosen with a mean of 63531.9 and a standard deviation of 3811.7 to test a new compound. set up a 95% confidence interval estimate for the new tire compound.

B.) Set up a 99% confidence interval estimate for the tire compound.

Answer 1

a)

sample mean, xbar = 63531.9
sample standard deviation, s = 3811.7
sample size, n = 16
degrees of freedom, df = n - 1 = 15

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.131

ME = tc * s/sqrt(n)
ME = 2.131 * 3811.7/sqrt(16)
ME = 2030.683

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (63531.9 - 2.131 * 3811.7/sqrt(16) , 63531.9 + 2.131 * 3811.7/sqrt(16))
CI = (61501.22 , 65562.58)

b)

sample mean, xbar = 63531.9
sample standard deviation, s = 3811.7
sample size, n = 16
degrees of freedom, df = n - 1 = 15

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.947

ME = tc * s/sqrt(n)
ME = 2.947 * 3811.7/sqrt(16)
ME = 2808.27

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (63531.9 - 2.947 * 3811.7/sqrt(16) , 63531.9 + 2.947 * 3811.7/sqrt(16))
CI = (60723.63 , 66340.17)