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 0.006 inch. After recalibrating theproduction machine, the manager randomly selects 29 pistons and determines that the standard deviation is 0.0053 inch. Is there significant evidence for the manager to conclude that the standard deviation hasdecreased at the a = 0.05 level of significance?What are the correct hypotheses for this test?The null hypothesis is Ho: o =0.006.The alternative hypothesis is H;:0.006.Calculate the value of the test statistic.= 21.85 (Round to two 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.)Enter your answer in the answer box and then click Check Answer.1part1 remainingClear AllCheck Answer

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 0.006 inch. After recalibrating the
production machine, the manager randomly selects 29 pistons and determines that the standard deviation is 0.0053 inch. Is there significant evidence for the manager to conclude that the standard deviation has
decreased at the a = 0.05 level of significance?
What are the correct hypotheses for this test?
The null hypothesis is Ho: o =
0.006.
The alternative hypothesis is H;:
0.006.
Calculate the value of the test statistic.
= 21.85 (Round to two 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.)
Enter your answer in the answer box and then click Check Answer.
1
part
1 remaining
Clear All
Check Answer

Expert Solution

Step 1 Introduction:

Test for Population Standard Deviation Chi-Square Test : Chi-Square Test is used to test the significance difference between Population Standard Deviation (Hypothesized value) and Sample Standard Deviation. Then the test statistic is denoted by $χ^{2}$ and it is given by

$χ^{2} = \frac{(n - 1) s^{2}}{σ^{2}}$

has a Chi-square distribution with (n-1) degrees of freedom.

where n is Sample size

s is Sample Standard Deviation

$σ$ is Population Standard Deviation

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