Answered: Managers at an automobile manufacturing…

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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Question

Managers at an automobile manufacturing plant would like to examine the mean completion time, μ , of an assembly line operation. The past data indicate that the mean completion time is 44 minutes, but the managers have good reason to believe that this value has decreased. The managers plan to perform a statistical test. After choosing a random sample of assembly line completion times, the managers compute the sample mean completion time to be

42 minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of 5 minutes.

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that the managers decide to reject the null hypothesis. What sort of error might they be making?
	▼(Choose one)
(c)	Suppose the true mean completion time for the assembly line operation is 44 minutes. Fill in the blanks to describe a Type I error.
A Type I error would be ▼(Choose one) the hypothesis that μ is ▼(Choose one) ▼(Choose one)when, in fact, μ is ▼(Choose one) .

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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