A purchuy 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 eleven projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the eleven machines is given in the table. Lifetimes of light bulbs (hours) Infocus 1142, 1028, 1083, 772, 890, 1025, 691, 813, 1001, 790, 916 Proxima 981, 849, 1101, 792, 1249, 836, 779, 1102, 1017, 756, 768 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 there is a difference in the mean lifetime of the light bulbs in the two brands? 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.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(a)	State the null hypothesis H0 and the alternative hypothesis H1 .
H0:
H1:
(b)	Determine the type of test statistic to use.
	▼(Choose one)
(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 there is a difference in the mean lifetimes of the light bulbs in the two brands?
Yes No

Transcribed Image Text:A purchuy 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 eleven projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the eleven machines is given in the table. Lifetimes of light bulbs (hours) Infocus 1142, 1028, 1083, 772, 890, 1025, 691, 813, 1001, 790, 916 Proxima 981, 849, 1101, 792, 1249, 836, 779, 1102, 1017, 756, 768 Send data to calculator Send data to Excel conclude, at the 0.05 level of Assume that the two populations of lifetimes are normally distributed and that the population variances are equal. Can significance, that there is a difference in the mean lifetime of the light bulbs in the two brands? 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.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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