Question

A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs, model A and model B. Independent random samples of the two models were taken. Analysis of 11 bulbs of model A showed a mean lifetime of 1345 hours and a standard deviation of 102 hours. Analysis of 15 bulbs of model B showed a mean lifetime of 1389 hours and a standard deviation of 82 hours. Assume that the populations of lifetimes for each model are normally distributed and that the variances of these populations are equal. Construct a 90% confidence interval for the difference u,-H, between the mean lifetime u, of model A bulbs and the mean lifetime uz of model B bulbs. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?

Answer 1

soli 0 Given Given that, A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs. Model A: Number of bulbs (n) = 11. Meanlife time of bulbs (X) = 1345 hours. Standard deviation ( s.) = 102 hours. Model B: Number of bulbs (12) - 15. Mean life time of bulbs (79) = 1389 hours. standard deviation (S2) = 82 hours. oomula for 100(1-0)4., confidence interval foo We know that, the formula for 100(1-2) 4., conto is confidence interval CCI) = (8x2) + thit n2-2 á Snitha Where, combine variance (s) is, sº = (0,-) + S + C -1)x s nit12-2 =(11-1) X(102) + (15-1) (82) 11+15-2 10 x(102) + 14682) 26-2 = 102X 1020 + 1148X82 24

104040 + 94136 24 = 8257.33 = J 8057.33 = es 90.869 p= 0.05 Anith2-2 = t 11 +15-2, a = = ta4, 0.05 2.063 c from Statistical table). 90% confidence Interval CCI) is Now, we need to calculate the C1 = (x - 2) + Fn +, -, * "n, no 90.869 X — = (1345 - 1389) + tgu 0.05 . V 11 +15 = -44 + 2.063 x — $* Vas! 90-869 = -44 -2.063 x 90.869 vać = -44 + 2.063 X 17.820 ,- 44 -2.063 X 17.820 = (-7.838 , -80.762) Lower limit for 904. (I upper limit for 90.4 CI = -80-762 = -7.238