Question

Six measurements were made of the magnesium ion concentration (in parts per million, 21) or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal. 188 135 160 173 183 168 Construct a 95% confidence interval for the mean magnesium ion concentration. A) 165.0 < μ < 170.7 B) 164.7 < μ < 171.0 C) 147.9 < μ < 187.8 D) 146.0 < μ < 189.7

Answer 1

sample mean, xbar = 167.83
sample standard deviation, s = 18.9886
sample size, n = 6
degrees of freedom, df = n - 1 = 5

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.571

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (167.83 - 2.571 * 18.9886/sqrt(6) , 167.83 + 2.571 * 18.9886/sqrt(6))
CI = (147.9 , 187.8)

Option C