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StatisticsQ&A LibraryA production line operation is tested for filling weight accuracy using the following hypotheses.HypothesisH 0: μ-16H a: μ 16Conclusion and ActionFilling okay, keep runningFilling off standard; stop and adjust machineThe sample size is 38 and the population standard deviation is σ = 1 . Use α = .05. Do not round intermediate calculations.a. What would a Type II error mean in this situation?Concluding that the mean filling weight is 16 ounces when it actually isn'tb. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?c. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?Question

Asked Apr 23, 2019

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Step 1

**b.**

**Type II error:**

Type II error is the failing to reject the null hypothesis when it is false.

Step 2

The null and alternative hypotheses are H_{0}: *µ *= 16 and H_{a}: *µ *≠ 16. A random sample of size 38 is taken from the population with standard deviation 1. The test is two tailed and the *Z*- value corresponding to significance level 0.05 is 1.96. Therefore, the probability of type II error is given by:

Step 3

Substituting *µ*0 = 16 and *σ *= 1, *n = *38 and the machine is overfilling by 0.5 ounces...

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