Question

A random sample of 43 Foreign Language movies made since 2000 had a mean length of 130.1 minutes, with a standard deviation of 12.1 minutes.

A)Construct a

98%  confidence interval for the true mean length of all Foreign Language movies made since 2000. Round the answers to one decimal place. A 98% confidence interval for the true meaning length of all Foreign language movies made since 2000 is

B) As of november 2013, three spider man movies have been released, and their mean is 129 minutes. Someone claims that the mean length of spider man movies is actually less then the mean length of all foreign language movies. Does the confidence interval contradict this claim

The confidence interval (does/does not) contradict this belief. Choose one

Answer 1

sample mean, xbar = 130.1
sample standard deviation, s = 12.1
sample size, n = 43
degrees of freedom, df = n - 1 = 42

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.418

ME = tc * s/sqrt(n)
ME = 2.418 * 12.1/sqrt(43)
ME = 4.462

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (130.1 - 2.418 * 12.1/sqrt(43) , 130.1 + 2.418 * 12.1/sqrt(43))
CI = (125.6 , 134.6)

A 98% confidence interval for the true meaning length of all Foreign language movies made since 2000 is between 125.6 and 134.6

b)

The confidence interval (does) contradict this belief