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 thirteen projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the thirteen machines is given in the table.

	Lifetimes of light bulbs (hours)
Infocus	724, 818, 1000, 709, 965, 696, 863, 934, 725, 974, 786, 893, 1026
Proxima	857, 756, 813, 1020, 802, 952, 888, 575, 994, 707, 730, 1100, 1087

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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

0.1

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)ZtChi squareF (PLEASE GIVE DEGREE OF FREEDOM 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

Answer 1

we have to test, At 0.1 level of significance, that there is a difference in the mean lifetime of the light bulbs in the two brands.

Here we use two sample t test assuming equal variances.

Hypothesis:

Ho: There is a no difference in the mean lifetime of the light bulbs in the two brands.

  

V/s

Ha: There is a difference in the mean lifetime of the light bulbs in the two brands.

  

(type of test statistic is two sample t test assuming equal variances)

Under Ho,

Where,

= sample mean for infocus and  = sample mean for proxima

Using Excel Data Analysis toolpack we solve this problem,

Infocus	proxima
724	857
818	756
1000	813
709	1020
965	802
696	952
863	888
934	575
725	994
974	707
786	730
893	1100
1026	1087

Excel => Data => Data Analysis => t-Test: Two-Sample Assuming Equal Variances => select input variables => Lables => alpha = 0.1 => output range => ok

t-Test: Two-Sample Assuming Equal Variances
	Infocus	proxima
Mean	854.8462	867.7692
Variance	14255.3077	24923.3590
Observations	13	13
Pooled Variance	19589.3333
Hypothesized Mean Difference	0
df	24
t Stat	-0.23540
P(T<=t) one-tail	0.40795
t Critical one-tail	1.31784
P(T<=t) two-tail	0.81589
t Critical two-tail	1.71088

Df for this test are,

n1+n2-2 = 13 + 13 - 2 = 24

Test statistic,

t = - 0.235

P-value is,

P-value = 0.816

Here p-value = 0.816 > alpha = 0.1 then we fail to reject Ho.

Can we conclude that there is a difference in the mean lifetimes of the light bulbs in the two brands? NO

I.e. we conclude that there is a no difference in the mean lifetimes of the light bulbs in the two brands.