Answered: The quality control manager at a light…

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 light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is
117 hours. A random sample of 81 light bulbs indicated a sample mean life of 370 hours. Complete parts (a) through (d) below.
a. Construct a 99% confidence interval estimate for the population mean life of light bulbs in this shipment.
The 99% confidence interval estimate is from a lower limit of 336.5 hours to an upper limit of 403.5 hours.
(Round to one decimal place as needed.)
b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 420 hours? Explain.

Based on the sample data, the manufacturer [does not have / has] the right to state that the lightbulbs have a mean life of 420 hours. A mean of 420 hours is [less than 2/more than 3]
standard errors [above/ below] the sample mean, so it is [likely/ highly unlikely]
that the lightbulbs have a mean life of 420 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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