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A bearing used in an automotive application is suppose to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard deviation \sigma =0.01 inch.
Test the hypotheses H0: \mu =1.5 versus H1: \mu \neq 1.5 using \alpha =0.01
(-) What sample size would be required to detect a true mean diameter as low as 1.495 inches if we wanted the power of the test to be at least 0.88?

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Answer:

We solve the issue in the following steps:-

Step-by-step explanation:

1) Interest parameter: the interest parameter is 'mu.' The value inside the Diameter.

2) Null hypotheses H0 ==> H0: u=1.5 inches

3) Alternative hypotheses: H1 u not equal 1.5 inches

4) Test statistics are

z0 = (x

5) Reject H0 if: rejects H0 if the P-value is less than 0.05. The limits of the critical region would be Z0.025 = 0.01 and-Z0.025 = -0.01 to use the fixed significance level test.

6) Computation :

Since x =1.4975, n=25 and Sigma =0.01

Z0 = (1.4975-1.5)/(0.01/ route of 25) = -1.25

7) Conclusion : since Z0=-1.25 the P value is

p value = 2[1-?(1.25)] = 0.2113

We deny H0: u=1.5 at a value of 0.01.

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