An automobile parts supplier owns a machine that produces a cylindrical engine part. This part is supposed to have an outside diameter of three inches. The technical staff feels that the mean diameter produced by the machine is off target. In order to verify this, a special study will randomly sample 40 parts produced by the machine. The 40 sampled parts will be measured, and if the results obtained cast a substantial amount of doubt on the hypothesis that the mean diameter equals the target value of three inches, the company will assign a problem-solving team to intensively search for the causes of the problem.Formula the hypotheses so that the problem-solving team will be assigned when the null hypothesis is rejected.A sample of 40 parts yields a sample mean diameter of 3.006 inches. Assume that the population standard deviation equals 0.016 inches. (1) Use the critical value approach to test H0 versus Ha when α = 0.05. (2) Use the p-value approach to test H0 versus Ha when α = 0.05.

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Description: An automobile parts supplier owns a machine that produces a cylindrical engine part. This part is supposed to have an outside diameter of three inches. The technical staff feels that the mean diameter produced by the machine is off target. In order t

1.State null and alternate hypotheses:Null hypothesis:Null hypothesis is a statement which is tested…

Answered: An automobile parts supplier owns 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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An automobile parts supplier owns a machine that produces a cylindrical engine part. This part is supposed to have an outside diameter of three inches. The technical staff feels that the mean diameter produced by the machine is off target. In order to verify this, a special study will randomly sample 40 parts produced by the machine. The 40 sampled parts will be measured, and if the results obtained cast a substantial amount of doubt on the hypothesis that the mean diameter equals the target value of three inches, the company will assign a problem-solving team to intensively search for the causes of the problem.
1. Formula the hypotheses so that the problem-solving team will be assigned when the null hypothesis is rejected.
2. A sample of 40 parts yields a sample mean diameter of 3.006 inches. Assume that the population standard deviation equals 0.016 inches. (1) Use the critical value approach to test H₀ versus H_a when α = 0.05. (2) Use the p-value approach to test H₀ versus H_a when α = 0.05.

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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