The piston diameter of a certain hand pump is 0.7 inch. The manager determines that the diameters are normally​distributed, 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​: ▼

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The piston diameter of a certain hand pump is
0.7 inch. The manager determines that the diameters are normally​distributed, 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​:
 
pp
sigmaσ
muμ
 
equals=
not equals≠
greater than>
less than<
 
0.005.
0.0033.
The alternative hypothesis is
H1​:
 
sigmaσ
pp
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.)
 
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