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 H 0: = 16 Filling okay, keep running H a: 16 Filling off standard; stop and adjust machine The sample size is 36 and the population standard deviation is = 1. Use = .05. Do not round intermediate calculations. What would a Type II error mean in this situation? 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

Here type II error mean that we fail to reject the null hypothesis even if it false that means we will fail to detect that in a production line operation which is tested for filling weight accuracy, the true filling amount is not 16 ounces.

Standard deviation = 1

standarded error of sample mean se0 = /sqrt(n) = 1/sqrt(36) = 1/6

we will reject the null hypothesis if sample mean x < 16 + Z95% se0 or x < 16 + 1.96 * 1/6 or x < 16.326667

Here true mean = 16.5 as machine is overfilling by 0.5 ounces

Pr(Type II error) = Pr(x < 16.326667 ; 16.5 ; 1/6)

Z = (16.326667 - 16.5)/(1/6) = -1.04

Pr(Type II error) = Pr(x < 16.326667 ; 16.5 ; 1/6) = Pr(Z < -1.04) = 0.1492

Power of the test = 1 - 0.1492 = 0.8508

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