A paint manufacturer fills cans of paint using a machine that has been calibrated to  fill the cans to contain an average of 1 gallon (128 ounces) each. To test whether their  machine has come out of calibration and overfills the cans, the manufacturer takes a random  sample of 81 cans. Assume the population standard deviation is 3.0 ounces, and the volume  of paint in the cans is normally distributed. Assume that, unknown to the researcher, the true  mean volume of the cans is 129 ounces. a)  What are the null and alternative hypotheses? b) For what values of should Ho be rejected so that the power of the test is 0.95?  What will the level then be? c) How large of a sample is needed so that a 1% level test has power 0.95?

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A paint manufacturer fills cans of paint using a machine that has been calibrated to 
fill the cans to contain an average of 1 gallon (128 ounces) each. To test whether their 
machine has come out of calibration and overfills the cans, the manufacturer takes a random 
sample of 81 cans. Assume the population standard deviation is 3.0 ounces, and the volume 
of paint in the cans is normally distributed. Assume that, unknown to the researcher, the true 
mean volume of the cans is 129 ounces.

a)  What are the null and alternative hypotheses?

b) For what values of should Ho be rejected so that the power of the test is 0.95? 
What will the level then be?

c) How large of a sample is needed so that a 1% level test has power 0.95?

 

 

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