Answered: The piston diameter of a certain hand…

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

The piston diameter of a certain hand pump is

0.7 inch. The manager determines that the diameters are normallydistributed, with a mean of 0.7 inch and a standard deviation of

0.005 inch. After recalibrating the production machine, the manager randomly selects 27 pistons and determines that the standard deviation is

0.0033 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the

α=0.10 level of significance?

What are the correct hypotheses for this test?

The null hypothesis is

H0:

▼

sigmaσ

muμ

▼

equals=

not equals≠

greater than>

less than<

▼

0.005.

0.0033.

The alternative hypothesis is

H1:

▼

sigmaσ

muμ

▼

not equals≠

equals=

less than<

greater than>

▼

0.005.

0.0033.

Calculate the value of the test statistic.

χ2 =

(Round to three decimal places as needed.)

Use technology to determine the P-value for the test statistic.

The P-value is=

(Round to three decimal places as needed.)

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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