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: mu = 16 Filling okay, keep running H_a: mu 16 Filling off standard; stop and adjust machine The sample size is 34 and the population standard deviation is sigma = 0.9. Use alpha = .05. a. What would a Type II error mean in this situation? b. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)? .4354 c. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)? .9981 d. What information does the power curve contain for the production manager? The probability of rejecting the null hypothesis for various mean filling weights.

Explanation / Answer

Answer:

MINITAB used.

Power and Sample Size

1-Sample Z Test

Testing mean = null (versus null)

Calculating power for mean = null + difference

= 0.05 Assumed standard deviation = 0.9

            Sample

Difference    Size     Power

       0.5   34     0.899631

b. Type II error =0.1004

c. Power = 0.8996

(power = 1- Type II error)

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