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Name: In a process that manufactures tungsten-coated silicon wafers, the tar
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Description: In a process that manufactures tungsten-coated silicon wafers, the target resistance for a wafer is 80 miliohms (??). In a simple random sample of 50 wafers, the sample mean resistance was 79. 8 miliohms (??) and the standard deviation was 0.5 milioh

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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In a process that manufactures tungsten-coated silicon wafers, the target resistance for a wafer is 80 miliohms (??). In a simple random sample of 50 wafers, the sample mean resistance was 79. 8 miliohms (??) and the standard deviation was 0.5 miliohms (??). Let ? (mu) represent the mean resistance of the wafers manufactured by this process. A quality engineer tests H0: ? (mu) = 80 versus H1: ?(mu) ≠ 80.

(a) Compute the test statistic.
(b) Assuming H0 is true, state the distribution of the test statistic.
(c) Compute the P − value of the test statistic.
(d) Using ?(alpha) = 0.05, do you believe it is plausible that the mean is on target, or are you convinced that the mean is not on target? Explain your reasoning.

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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