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

See similar textbooks

Related questions

Question

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 84 hours. A random sample of 49 light bulbs indicated a sample mean life of 270 hours.

Suppose the standard deviation changes to 63
hours. What are your answers in (a) and (b)?

The 95% confidence interval estimate would be from a lower limit of ______
hours to an upper limit of _______ hours.

My answer for (a) is:

The 95% confidence interval estimate is from a lower limit of

246.5 hours to an upper limit of 293.5 hours.

My answer for (b) is:

Based on the sample data, the manufacturer

does not have the right to state that the lightbulbs have a mean life of

320 hours. A mean of 320 hours is more than 4 standard errors above

the sample mean, so it is highly unlikely that the lightbulbs have a mean life of 320 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 + ...

Expert Solution