The piston diameter of a certain hand pump is 0.5inch. The manager determines th

Question

The piston diameter of a certain hand pump is 0.5inch. The manager determines that the diameters are normallydistributed, with a standard deviation of 0.008 inch. Afterrecalibration the production machine, the manager randomly selects20 pistons and determines that the standard deviation is 0.0064inch. Is there sufficient evidence for the manager toconclude that the standard deviation has decreased at the= 0.05 level of significance?   What is the critical value? The piston diameter of a certain hand pump is 0.5inch. The manager determines that the diameters are normallydistributed, with a standard deviation of 0.008 inch. Afterrecalibration the production machine, the manager randomly selects20 pistons and determines that the standard deviation is 0.0064inch. Is there sufficient evidence for the manager toconclude that the standard deviation has decreased at the= 0.05 level of significance?   What is the critical value?

Explanation / Answer

Ho:2=(.008)2=.000064 H1:2<.000064 Test statistic is chi-square X2=(n-1)S2/2   with n-1 degrees of freedom Critical valueis X2.95=10.12. So reject if X2 is less than 10.12 X2=19(.0064)2/.000064=12.16 Evidence is not conclusive. Critical valueis X2.95=10.12. So reject if X2 is less than 10.12 X2=19(.0064)2/.000064=12.16 Evidence is not conclusive.

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