A light bulb manufacturer wants to compare the mean lifetimes of two of its ligh

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 1280 hours and a standard deviation of 90 hours. Analysis of 14 bulbs of model B showed a mean lifetime of 1287 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 95% confidence interval for the difference mu_1 - mu_2 between the mean lifetime mu_1 of model A bulbs and the mean lifetime mu_2 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.)

Explanation / Answer

The statistical software output for this problem is:

Two sample T confidence interval:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
(with pooled variances)

95% confidence interval results:

Hence,

Lower limit of 95% confidence interval: -78.32

Upper limit of 95% confidence interval: 64.32

Difference Sample Diff. Std. Err. DF L. Limit U. Limit 1 - 2 -7 34.47722 23 -78.321564 64.321564

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