Question

The UW student-athletes on the women's teams compete in various NCAA-I sports. Each team may be regarded as a random sample of all the NCAA-I athletes in that sport. The 14 players listed on the roster for the 2004-05 Women’s Basketball team had an average height of 69.67 inches with a standard deviation of 3.47 inches. Give a 99% confidence interval for the average height of NCAA-I women’s basketball players in that year. Write a one or two sentence summary in non-statistical language to describe what you have found, not how you found it. Your audience is people who have never had a statistics class (think of middle of the road 8th graders, not the really bright ones).

Answer 1

sample mean, xbar = 69.67
sample standard deviation, s = 3.47
sample size, n = 14
degrees of freedom, df = n - 1 = 13

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.012

ME = tc * s/sqrt(n)
ME = 3.012 * 3.47/sqrt(14)
ME = 2.793

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (69.67 - 3.012 * 3.47/sqrt(14) , 69.67 + 3.012 * 3.47/sqrt(14))
CI = (66.88 , 72.46)

Therefore, based on the data provided, the 99% confidence interval for the population mean is 66.88 < μ < 72.46 which indicates that we are 99% confident that the true population mean μ is contained by the interval (66.88 , 72.46)