Description
A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip their classrooms. Of major concern is the
longevity of the light bulbs used in the projectors. The purchasing manager has narrowed down the choice of projector to two brands, Infocus and
Proxima, and wishes to determine if there is any difference between the two brands in the mean lifetime of the bulbs used.
The purchasing manager obtained twelve projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted
on each of the twelve projectors is given in the table.
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Assume that the two populations of lifetimes are normally distributed and that the population variances are equal.
Can we conclude, at the 0.01 level of significance, that 𝜇1, the mean lifetime of light bulbs in Infocus projectors, differs from 𝜇2, the mean lifetime of
light bulbs in Proxima projectors?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of
formulas.)
(a) State the null hypothesis 𝐻0 and the alternative hypothesis 𝐻1.
𝐻0:
𝐻1:
(b) Determine the type of test statistic to use.
(Choose one) grad
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the 𝑝-value. (Round to three or more decimal places.)
(e) Can we conclude that 𝜇1, the mean lifetime of light bulbs in Infocus
projectors, differs from 𝜇2, the mean lifetime of light bulbs in Proxima
projectors?
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