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.

The sample size is 31 and the population standard deviation is  = 0.6. Use  = .05. Do not round intermediate calculations.

a. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?

b. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?

Hypothesis Conclusion and Action H 0:  = 16 Filling okay, keep running H a: 16 Filling off standard; stop and adjust machine

Explanation / Answer

Result:

MINITAB used

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 31 and the population standard deviation is  = 0.6. Use  = .05. Do not round intermediate calculations.

a. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?

Power and Sample Size

1-Sample t Test

Testing mean = null (versus null)

Calculating power for mean = null + difference

= 0.05 Assumed standard deviation = 0.6

Results

Difference

Sample
Size

Power

0.5

31

0.994245

Type II error = 1-power = 1-0.994245 =0.005755

=0.0058

b. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?

Power = 0.9942

Hypothesis

Conclusion and Action

H 0:  = 16

Filling okay, keep running

H a: 16

Filling off standard; stop and adjust machine

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