A production line operation is tested for filling weight accuracy using the foll

Question

A production line operation is tested for filling weight accuracy using the following hypotheses. Hypothesis Conclusion and Action H0: = 16 Filling okay, keep running Ha: 16 Filling off standard; stop and adjust machine The sample size is 40 and the population standard deviation is = 0.7. Use = .05. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)? What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?

Explanation / Answer

The sign in alternative hypothesis is not displayed. Assume it to b eleft tailed test.

Therefore, on ecommit sType II error if one get Z statistic more than -1.64. Find X critical by solving th efollowing equation.

-1.64=(Xcritical-mu)/sigmax=(Xcritical-16.5)/(0.7/sqrt 40)

Xcritical=16.3196

P(Z>[(16.3196-16)/0.11]

P(Z>2.90]=0.0019

Power of test is 1-0.0019=0.9981

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