Answered: Industrial light bulbs should have a…

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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Question

Industrial light bulbs should have a mean life length acceptable to potential users and a relatively
small variation in life length. If some bulbs fail too early in their life, users become annoyed and are
likely to switch to bulbs produced by a different manufacturer. Large variations above the mean
reduce replacement sales; in general, variation in life lengths disrupts the user’s replacement
schedules. A random sample of 20 bulbs produced by a particular manufacturer produced the
following lengths of life (in hours):
2100, 2302, 1951, 2067, 2415, 1883, 2101, 2146, 2278, 2019,
1924, 2183, 2077, 2392, 2286, 2501, 1946, 2161, 2253, 1827.
(a) Find a 99% confidence interval for the standard deviation of the lengths of life for the bulbs
produced by this manufacturer.
(b) Is the true population standard deviation possibly less than 150 hours? Why or why not?

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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