Question

Calculate the 95% confidence interval for μ given the random sample below:

16

13

14

14

Fill in the blanks for the CI: Estimate ± Critical Value × Standard Error

x¯± t* ×s/n

["57.00", "19.00", "14.25"]     ± ["1.96", "3.182", "2.776"]    ×

["1.26", "1.88", "1.09"]         /SQRT( ["4", "3", "5"]         )

95%CI for μ ( ["12.2, 16.3", "10.2, 18.3", "17.8, 20.2"]         )

Answer 1

sample mean, xbar = 14.25
sample standard deviation, s = 1.26
sample size, n = 4
degrees of freedom, df = n - 1 = 3

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 3.182

ME = tc * s/sqrt(n)
ME = 3.182 * 1.26/sqrt(4)
ME = 2.005

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (14.25 - 3.182 * 1.26/sqrt(4) , 14.25 + 3.182 * 1.26/sqrt(4))
CI = (12.2 , 16.3)

x¯± t* ×s/n = 14.25 +/- 3.182 * 1.26/sqrt(4))

95%CI for μ ( ["12.2, 16.3",