The piston diameter of a certain hand pump is0.4inch. The manager determines that the diameters are normally distributed, with a mean of0.4inch and a standard deviation of0.007inch. After recalibrating the production machine, the manager randomly selects27pistons and determines that the standard deviation is0.0061inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at theα=0.01level of significance?1. Calculate the test statistic X2 =?2. What is the p-value?

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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The piston diameter of a certain hand pump is

0.4

inch. The manager determines that the diameters are normally distributed, with a mean of

0.4

inch and a standard deviation of

0.007

inch. After recalibrating the production machine, the manager randomly selects

pistons and determines that the standard deviation is

0.0061

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

α=0.01

level of significance?

1. Calculate the test statistic X²=?

2. What is the p-value?

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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