A 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)?

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Asked Apr 23, 2019
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A production line operation is tested for filling weight accuracy using the following hypotheses.
Hypothesis
H 0: μ-16
H a: μ 16
Conclusion and Action
Filling okay, keep running
Filling off standard; stop and adjust machine
The 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't
b. 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)?
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A production line operation is tested for filling weight accuracy using the following hypotheses. Hypothesis H 0: μ-16 H a: μ 16 Conclusion and Action Filling okay, keep running Filling off standard; stop and adjust machine The 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't b. 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)?

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Expert Answer

Step 1

b.

Type II error:

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

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Step 2

The null and alternative hypotheses are H0: µ = 16 and Ha: 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:

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Step 3

Substituting µ0 = 16 and σ = 1, n = 38 and the machine is overfilling by 0.5 ounces...

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