Question

A study by the International Coffee Organisation found that persons aged30 –59 drank an average of 0.57 cups of coffee per day. Assuming that the sample size is 200 with a sample standard deviation of 0.4 cups, construct a 95% confidence interval for the population mean cup of coffee. Interpret your answer.

Answer 1

sample mean, xbar = 0.57
sample standard deviation, s = 0.4
sample size, n = 200
degrees of freedom, df = n - 1 = 199

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.972

ME = tc * s/sqrt(n)
ME = 1.972 * 0.4/sqrt(200)
ME = 0.056

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (0.57 - 1.972 * 0.4/sqrt(200) , 0.57 + 1.972 * 0.4/sqrt(200))
CI = (0.5142 , 0.6258)
Therefore, based on the data provided, the 95% confidence interval for the population mean is 0.5142 < μ < 0.6258 which indicates that we are 95% confident that the true population mean μ is contained by the interval (0.5142 , 0.6258)