Question

A medical study followed a SAMPLE of 12 heart patients who had received electronic pacemakers. The time (in months) to the first electrical malfunction was recorded: 12 16 24 14 22 16 32 14 22 8 20 10 (a) Calculate the estimated standard error of the mean ( two decimal places ) (5pts) (b)Determine the critical value for a t space space f o r space alpha space equals space 0.02 space left parenthesis space 2 space t a i l space t e s t right parenthesis. (2pts) (c) Find the 98% confidence for the population mean (5 pts)

Answer 1

a)

sample standard deviation, s = 6.7756
sample size, n = 12

std.error = 6.7756/sqrt(12)
= 1.9559

b)

sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.718

Critical value = 2.718
c)

sample mean, xbar = 17.5
sample standard deviation, s = 6.7756
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.718

ME = tc * s/sqrt(n)
ME = 2.718 * 6.7756/sqrt(12)
ME = 5.316

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (17.5 - 2.718 * 6.7756/sqrt(12) , 17.5 + 2.718 * 6.7756/sqrt(12))
CI = (12.18 , 22.82)