The piston diameter of a certain hand pump is 0.5 inch. The manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.005 inch. After recalibrating the production machine, the manager randomly selects 25 pistons and determines that the standard deviation is 0.0034 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α=0.10 level of significance?
The piston diameter of a certain hand pump is 0.5 inch. The manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.005 inch. After recalibrating the production machine, the manager randomly selects 25 pistons and determines that the standard deviation is 0.0034 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α=0.10 level of significance?
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Part 1
What are the correct hypotheses for this test?
The null hypothesis is H0:
sigmaσ
sigmaσ
muμ
pp
equals=
greater than>
less than<
not equals≠
equals=
0.005.
0.005.
0.0034.
The alternative hypothesis is H1:
sigmaσ
muμ
pp
sigmaσ
less than<
greater than>
not equals≠
equals=
less than<
0.005.
0.0034.
0.005.
Part 2
Calculate the value of the test statistic.
χ2 =enter your response here (Round to three decimal places as needed.)
Part 3
Use technology to determine the P-value for the test statistic.
The P-value is enter your response here.
(Round to three decimal places as needed.)
Part 4
What is the correct conclusion at the α=0.10 level of significance?
Since the P-value is
▼
greater
less
than the level of significance,
▼
reject
do not reject
the null hypothesis. There
▼
is
is not
sufficient evidence to conclude that the standard deviation has decreased at the 0.10 level of significance.
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