. The University of Washington uses thousands of BrightLight fluorescent light bulbs each year. A new manufacturer, AmpleLamp, claims that its new brand of bulbs, which cost the same as the brand the university currently uses, has a mean life of 6000 hours. The university has never studied how long BrightLight bulbs last and they decided they are curious to see how long BrightLight bulbs last compared to AmpleLamp bulbs. They university decides to conduct a significance test at the .05 significance level. A random sample of 64 BrightLight bulbs are tested and the mean life time is found to be 5910 hours. Both manufacturers report that the standard deviation for the lifespan of a light is 400 hours. Are the lifespan of the two brands of lights significantly different from each other? Use α =0.1 (a) Which of the following is the H0 ? (null) A.H0:μ = 6000 B.H0:x = 6000 C.H0:μ = 5910 D.H0:x = 5910 E.H0:μ ̸= 6000 F.H0:x ̸= 6000 G.H0:μ ̸= 5910 H.H0:x ̸= 5910 I. None of these Hint: First read the problem and using my notes (or Hawkes) for 9.5, set up H0 and Ha . Then pick the right Ha from the above list. Dont try to guess the answer from the above list. (b) Which of the following is the correct formula to compute Test Statistic (TS)? 6000 − 5910 A. √ 400/ 64 5910 − 6000 B. √ 400/ 64 6000 − 5910 C. √ 20/ 64 Page 2 5910 − 6000 D. √ 20/ 64 E. None of these (c) What is the value of Test Statistic (TS)? (d) What is the critical value from Critical Table? (e) What is the p-value ? (f) Conclusion A. Reject H0 B. Fail to reject H0 (g) Interpretation There is enough evidence (from data) in support of AmpleLamp claim that both have the same mean life. There is not enough evidence (from data) in support AmpleLamp claim that both have the same mean life.

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Description: 2. The University of Washington uses thousands of BrightLight fluorescent light bulbs each year. A new manufacturer, AmpleLamp, claims that its new brand of bulbs, which cost the same as the brand the university currently uses, has a mean life of 600

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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2. The University of Washington uses thousands of BrightLight fluorescent light bulbs each year. A new manufacturer, AmpleLamp, claims that its new brand of bulbs, which cost the same as the brand the university currently uses, has a mean life of 6000 hours. The university has never studied how long BrightLight bulbs last and they decided they are curious to see how long BrightLight bulbs last compared to AmpleLamp bulbs. They university decides to conduct a significance test at the .05 significance level. A random sample of 64 BrightLight bulbs are tested and the mean life time is found to be 5910 hours. Both manufacturers report that the standard deviation for the lifespan of a light is 400 hours. Are the lifespan of the two brands of lights significantly different from each other? Use α =0.1

(a) Which of the following is the H0 ? (null) A.H0:μ = 6000

B.H0:x = 6000 C.H0:μ = 5910 D.H0:x = 5910 E.H0:μ ̸= 6000 F.H0:x ̸= 6000 G.H0:μ ̸= 5910 H.H0:x ̸= 5910

I. None of these

Hint: First read the problem and using my notes (or Hawkes) for 9.5, set up H0 and Ha . Then pick the right Ha from the above list. Dont try to guess the answer from the above list.
(b) Which of the following is the correct formula to compute Test Statistic (TS)?

6000 − 5910 A. √

400/ 64

5910 − 6000 B. √

400/ 64

6000 − 5910 C. √

20/ 64

Page 2

5910 − 6000 D. √

20/ 64
E. None of these

(d) What is the critical value from Critical Table?
(e) What is the p-value ?
(f) Conclusion

A. Reject H0 B. Fail to reject H0
(g) Interpretation
1. There is enough evidence (from data) in support of AmpleLamp claim that both have the same mean life.
2. There is not enough evidence (from data) in support AmpleLamp claim that both have the same mean life.

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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