Question

75 The manufacture of large liquid crystal displays (LCD's) is difficult. Some defects are minor and can be removed; others are unremovable. The number of unremovable defects, for each of n = 45 displays (Courtesy of Shiyu Zhou) 10 5 3 0 7 600 4 6 8 5 0 9 1 0 8 6 0 3 2 0 0 0 6 0 10 0 6 0 0 1 0 0 0 0 1 5 1 0 5 0 0 2 has T = 2.467 and s = 3.057 unremovable defects. What can one assert with 98% confidence about the maximum error if = 2.467 is used as a point esti- mate of the true population mean number of unremov- able defects? 726 With reference to the previous exercise, construct a 98% confidence interval for the true population mean number of unremovable defects per display.

help me please

Answer 1

sample mean, xbar = 2.467
sample standard deviation, s = 3.057
sample size, n = 45
degrees of freedom, df = n - 1 = 44

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.414

ME = tc * s/sqrt(n)
ME = 2.414 * 3.057/sqrt(45)
ME = 1.1001

X - te X X te x Vn CI n

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (2.467 - 2.414 * 3.057/sqrt(45) , 2.467 + 2.414 * 3.057/sqrt(45))
CI = (1.3669 , 3.5671)