Answered: An automobile assembly line operation…

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

An automobile assembly line operation has a scheduled mean completion time, μ , of 13.6 minutes. The standard deviation of completion times is

1.5 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of

46 completion times under new management was taken. The sample had a mean of 13.5 minutes. Assume that the population is normally distributed. Can we support, at the

0.05

level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.

a)	State the null hypothesis H0? and the alternative hypothesis H1? .
H0:?
H1:?
(b)	Determine the type of test statistic to use.
	▼(Choose one) chi sqaure ? z ? t ? f?
(c)	Find the value of the test statistic. ? (Round to three or more decimal places.)

(d)	Find the p-value. ?(Round to three or more decimal places.)

(e)	Can we support the claim that the mean completion time has decreased under new management? yes or no ?

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

Step 1

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a) Hypothesis:

The null hypothesis is,

$H_{0} : μ = 13.6$

The alternative hypothesis is,

$H_{1} : μ < 13.6$

The type of test statistic to be used is Z as, the population is distributed normally with known population standard deviation.

For testing mean with known population standard deviation Z test is most appropriate test.

Answer:

Thus, the type of test statistic to be used is Z.

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