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 31 and the population standard deviation is  = 1. Use  = .05. Do not round intermediate calculations.

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

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

Answer 1

Given data

n=33

population standard deviation () = 1

significance level () =0.05

To find the Type II error mean in this situation:

Concluding that the mean filling weight is 16 ounces when it actually is n't

To find the probability of making a Type II error when the machine is overfilling by .5 ounces:

lower cut off sample mean=

upper cut off sample mean=

when true mean is 16.5

P(type II error)=P(-4.83

=P(z<-0.91)-P(z<-4.83)

= (1−P ( Z<0.91 )) - (1-p(Z<4.83)

= (1-0.8186) -( 1-1)

= 0.1814

P(type II error) = 0.1814

To find the power of the statistical test when the machine is overfilling by .5 ounces:

Power=1-P(type II error)

=1-0.1814

=0.8186

Therefore the power of the statistical test when the machine is overfilling by .5 ounces is 0.8186