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 nine projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the nine projectors is given in the table. Lifetimes of light bulbs (hours) Infocus 933, 972, 1046, 931, 1027, 1045, 772, 986, 830 Proxima 783, 842, 939, 1009, 648, 676, 1046, 661, 1158 Send data to calculator Send data to Excel Assume that the two populations of lifetimes are normally distributed and that the population variances are equal. Can we conclude, at the 0.05 level of significance, thatu,, the mean lifetime of light bulbs in Infocus projectors, differs from u, 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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Transcribed Image Text: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 nine projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the nine projectors is given in the table. Lifetimes of light bulbs (hours) Infocus 933, 972, 1046, 931, 1027, 1045, 772, 986, 830 Proxima 783, 842, 939, 1009, 648, 676, 1046, 661, 1158 Send data to calculator Send data to Excel Assume that the two populations of lifetimes are normally distributed and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that u,, the mean lifetime of light bulbs in Infocus projectors, differs from u, 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 H, and the alternative hypothesis H,.
H :0
H1 :0
(b) Determine the type of test statistic to use.
(Choose one) ▼
OSO
(c) Find the value of the test statistic. (Round to three or more decimal places.)
ロメロ
O<O
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can we conclude that u,, the mean lifetime of light bulbs in Infocus
projectors, differs from ul,, the mean lifetime of light bulbs in Proxima
projectors?
O Yes ONo
P.

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