Question

A random sample of 16 pharmacy customers showed the waiting times below (in minutes).

21	22	22	17	21	17	23	20
20	24	9	22	16	21	22	21

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Find a 90% confidence interval for μ, assuming that the sample is from a normal population. (Round your standard deviation answer to 4 decimal places and t-value to 3 decimal places. Round your final answers to 3 decimal places.)

The 90% confidence interval ___ to ___

Answer 1

sample mean, xbar = 19.875
sample standard deviation, s = 3.6492
sample size, n = 16
degrees of freedom, df = n - 1 = 15

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.753

ME = tc * s/sqrt(n)
ME = 1.753 * 3.6492/sqrt(16)
ME = 1.599

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (19.875 - 1.753 * 3.6492/sqrt(16) , 19.875 + 1.753 * 3.6492/sqrt(16))
CI = (18.276 , 21.474)

The 90% confidence interval 18.276 to 21.474