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Name: A machine is set to produce bolts with a mean length of 1 inch. Bolts
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Description: A machine is set to produce bolts with a mean length of 1 inch. Bolts that are too long or too short do not meet the customer’s specifications and must be rejected. To avoid producing too many rejects, the bolts produced by the machine are sampled fr

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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A machine is set to produce bolts with a mean length of 1 inch. Bolts that are too long or too short do not meet the customer’s specifications and must be rejected. To avoid producing too many rejects, the bolts produced by the machine are sampled from time to time and tested as a check to see whether the machine is still operating properly. Suppose fifty-one bolts have been sampled, and x =1.02 and s=.04. Do the data provide sufficient evidence to conclude that the machine is producing bolts with a mean length not equal to 1 inch? Conduct hypothesis test using a=.05. Use the traditional approach and the p-value approach to hypothesis testing! Show all of the steps of the hypothesis test for each approach.

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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