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 39 and the population standard deviation is  = 0.9. Use  = .05. Do not round intermediate calculations.

1. What would a Type II error mean in this situation?
   SelectConcluding that the mean filling weight is not 16 ounces when it actually isConcluding that the mean filling weight is 16 ounces when it actually isn'tItem 1  
   
2. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?
     
   
3. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?
     
   
4. Choose the power curve for this hypothesis test.

Answer 1

Given data es Ho: M=16 Vs Ha: H+16 n=39 O=0.9 & Q=0:05 a) is 16 ounces concluding corresponding P (Type ll error) = P(Z < 74/2 + olio ) M-hal M-Ma + 0.5 ainces that the mean Helling weight Because type I error occur when we fell to reject the null hypothesis, when it is false. by this test as a two toliled test, so the z-value the significance level 0.05 is £1.96 Therefore the probability of type II error is ; -)-p(22-2 -Plz 2-1/2 olin bence, Ma = 16 +0.5 = 16-5 as machine as overfilling by P(Type 11 error) =p =P(221-96 0.9239 -plec 0.96124 =P(z<1.96+(-3-4694-))-P(24-196 +(3-4674 =P(24(1.96-3.4690) -P[<<<1-96 - 3.4694) = P(Z2-1-5074)-P(24-5.4294) = P(ZC-151)-P[2C -5.43) PC type II error) = 206552 -0.0000 i ptypell error) - 0.06ES complementary 16-16-5 1-96 + 16 - 16:59 <-1967 of the C power of the test is probability of type II error so poweo of the test | --O-0655 -0.9345