Question

The Hobbit: an Unexpected Journey extended gift-set edition was released back in 2013. The prices recorded from a number of on-line retailers were:
$54.74 $56.93 $54.01 $56.94 $55.94 $62.95 $68.95
Assuming that the prices listed above are from a SRS of a normal population of all on-line retailers, calculate a 95% confidence interval for the mean price. Show your work. Be sure to mention the value of df if it is relevant

Answer 1

sample mean, xbar = 58.64
sample standard deviation, s = 5.3948
sample size, n = 7
degrees of freedom, df = n - 1 = 6

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.447

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (58.64 - 2.447 * 5.3948/sqrt(7) , 58.64 + 2.447 * 5.3948/sqrt(7))
CI = (53.65 , 63.63)