Question

A production line operation is tested for filling weight accuracy using the following hypotheses. Hypothesis Ho: 1 = 16 Hai + 16 conclusion and Action Filling okay, keep running Filling off standard; stop and adjust machine The sample size is 32 and the population standard deviation is o = 0.9. Use a = .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)? .0923 ♡ c. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)? 0.9077 ®

Answer 1

b) Probability of Type -II error = P (fail to reject H0|H0 is false) = P(fail to reject H0|H1 is True)

Sample size (n) =32

$\sigma$= 0.9

$\alpha$= 0.5

Probability of making type 2 error when machine is filling by 0.5 ounces more

1 - 1

z= 16.5-16/(0.9/sqrt(32))=3.14269

From Normal distribution table for this Z value the probability <= 3.14269 = NORM.S.DIST(3.16269,TRUE) = 0.999163

Probability of makingtype -II error ($\beta$)= upper tail = 1-0.999163= 0.0008

b) Power of the test = 1-$\beta$= 0.9992 (up to 4 decimal places)

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