Question

= 25 hours. A random sample of 22 bulbs The life in hours of a 75-watt light bulb is known to be normally distributed with has a mean life of K = 1014 hours. (a) Construct a 95% two-sided confidence interval on the mean life. Round your answers to the nearest integer (e.g. 9876). (b) Construct a 95% lower-confidence bound on the mean life. Compare the lower bound of this confidence interval with the one in part (a). Round your answer to the nearest integer (e.g. 9876). exact number, no tolerance

Answer 1

A)

sample mean, xbar = 1014
sample standard deviation, σ = 25
sample size, n = 22

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 25/sqrt(22)
ME = 10.45

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (1014 - 1.96 * 25/sqrt(22) , 1014 + 1.96 * 25/sqrt(22))
CI = (1004 , 1024)

B)
Z Value at 95% = 1.64

lower bound = mean - z *(s/sqrt(n))
= 1014 - 1.64 *(25/sqrt(22))
= 1005