4. A bearing ball manufacturer is under the assumption that they are producing b

Question

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 Aum. What is the conclusion of the test?

Explanation / Answer

(A)
In order to verify the bearing diameter below are the null and alternate hypothesis

H0: mu <= 60
H1: mu > 60

Test statistics to be used is z.
For 0.05 significance level, z-critical value is 1.64.

for the sample mean 60.5
z = (60.5 - 60)/(4/sqrt(100)) = 1.25

p-value = 0.1057

As p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

(C)
there is possibility of commiting Type II error where not rejecting null hypothesis thought it is not true.

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