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,: o 0.006, Calculate the value of the test statistic. Xổ = 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. part remaining Clear All Check Answer

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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
Transcribed Image Text: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 χ2 and it is given by

χ2=(n-1)s2σ2

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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