A purchasing manager for a large university is investigating which brand of LCD

Question

A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip "smart" 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 ten projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the ten machines is given in the table.

751, 958, 809, 687, 1055, 964, 992, 912, 740, 1040

898, 775, 656, 907, 981, 659, 1040, 869, 691, 567

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 there is a difference in the mean lifetime of the light bulbs in the two brands?

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a  list of formulas.)

The null hypothesis:

H0:

The alternative hypothesis:

H1:

The type of test statistic:

(Choose one)Z,t,Chi-square,F

The value of the test statistic:
(Round to at least three decimal places.)

The p-value:
(Round to at least three decimal places.)

Can we conclude that there is a difference in the mean lifetimes of the light bulbs in the two brands?

Yes

No

p

x

s

p

Lifetimes of light bulbs (hours) Infocus

751, 958, 809, 687, 1055, 964, 992, 912, 740, 1040

Proxima

898, 775, 656, 907, 981, 659, 1040, 869, 691, 567

Explanation / Answer

Here we will perform t test with equal variances.

H0 : 1 = 2

Ha : 1 2

The typeof test statistic is t test

HEre the excel output is given below

Here test statistic

t = 1.3248

p - value= 0.2018

We cannot conclude that there is a difference in the mean lifetimes of the light bulbs in the two brands

t-Test: Two-Sample Assuming Equal Variances Infocus Proxima Mean 890.8 804.3 Variance 17810.8444 24822.4556 Observations 10 10 Pooled Variance 21316.65 Hypothesized Mean Difference 0 df 18 t Stat 1.3248 P(T<=t) one-tail 0.1009 t Critical one-tail 1.7341 P(T<=t) two-tail 0.2018 t Critical two-tail 2.1009

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