The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. A random sample of 64 CFLs indicates a sample mean life of 7,250 hours. Match the followings concepts to their correct interpretations in the context of the question: Null hypothesis Alternative hypothesis Type I error Type II error A. The mean life of a large shipment of CFLs is equal to 7,500 hours. B. The mean life of a large shipment of CFLs is equal to 7,500 hours and you conclude that it is not equal to 7,500 hours. C. The mean life of a large shipment of CFLs is not equal to 7,500 hours. D. The mean life of a large shipment of CFLs is not equal to 7,500 hours and you conclude that it is equal to 7,500 hours.

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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The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. A random sample of 64 CFLs indicates a sample mean life of 7,250 hours.

Match the followings concepts to their correct interpretations in the context of the question:

	Null hypothesis
	Alternative hypothesis
	Type I error
	Type II error

A.	The mean life of a large shipment of CFLs is equal to 7,500 hours.
B.	The mean life of a large shipment of CFLs is equal to 7,500 hours and you conclude that it is not equal to 7,500 hours.
C.	The mean life of a large shipment of CFLs is not equal to 7,500 hours.
D.	The mean life of a large shipment of CFLs is not equal to 7,500 hours and you conclude that it is equal to 7,500 hours.

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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