Posted question 4 for reference, only need answer for question 6. Thanks. 4. A b

Question

Posted question 4 for reference, only need answer for question 6. Thanks.

4. A bearing ball manufacturer is under the assumption that they are producing bearing balls of diameter 60 um. Of course the actual diameters are normally distributed with mean 60 and variance of 16. Recently there are more than usual number of boxes of the bearing returned to the factory as the diameters exceeded certain threshold level. we suspect that our machines may be out of calibration and the mean of diameters may have gradually exceeded 60um. a) We take a sample of n 100 bearings to run a test of hypothesis. Determine the 'test statistic for this hypothesis testing, and the critical values related to the significance level 0.05. b) Suppose the sample mean is 60.5 pum. What is the conclusion of the test?

Explanation / Answer

here we can apply chi distribution for which values at 0.025 and 0.975 percentile for 60 degree of freedom are 83.298 and 40.482

hence lower critical value =40.482*16/60 =10.7951

and lower critical values =83.298*16/60=22.2127

if S2 comes outside of this value our orignial calim for variance is no longer valid

please revert

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