The piston diameter of a certain hand pump is 0.6 inch. The manager determines that the diameters are normally​ distributed, with a mean of 0.6 inch and a standard deviation of 0.007 inch. After recalibrating the production​ machine, the manager randomly selects 27 pistons and determines that the standard deviation is 0.0052 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​: sigma equals 0.003. The alternative hypothesis is H1​: (sigma less than) = Calculate the value of the test statistic. x^2 = ​(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.) What is the correct conclusion at the level of​ significance? Since the​ P-value is less than the level of​ significance, do not reject the null hypothesis. There is sufficient evidence to conclude that the standard deviation has decreased at the level of significance

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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The piston diameter of a certain hand pump is

0.6

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

0.6

inch and a standard deviation of

0.007

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

27

pistons and determines that the standard deviation is

0.0052

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​: 
sigma
equals
0.003.
The alternative hypothesis is H1​: (sigma less than)   = 


Calculate the value of the test statistic.

x^2 =  

​(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.)

What is the correct conclusion at the  level of​ significance?

Since the​ P-value is less than the level of​ significance,  do not reject the null hypothesis. There is sufficient evidence to conclude that the standard deviation has decreased at the  level of significance

 

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