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.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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