Question

Confidence Interval for μ: You poll 25 students and record each student’s height. You find that the average height is 60 inches with a standard deviation of 4 inches.

a) Compute a 95% Confidence Interval for the mean height (μ) for this population of students.

b) Compute a 99% Confidence Interval for the mean height (μ) for this population of students.

Answer 1

a)

sample mean, xbar = 60
sample standard deviation, s = 4
sample size, n = 25
degrees of freedom, df = n - 1 = 24

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.064

ME = tc * s/sqrt(n)
ME = 2.064 * 4/sqrt(25)
ME = 1.651

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (60 - 2.064 * 4/sqrt(25) , 60 + 2.064 * 4/sqrt(25))
CI = (58.35 , 61.65)

b)

sample mean, xbar = 60
sample standard deviation, s = 4
sample size, n = 25
degrees of freedom, df = n - 1 = 24

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.797

ME = tc * s/sqrt(n)
ME = 2.797 * 4/sqrt(25)
ME = 2.238

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (60 - 2.797 * 4/sqrt(25) , 60 + 2.797 * 4/sqrt(25))
CI = (57.76 , 62.24)