Inference - type 2 error 3. A soda vending machine is scheduled to ship an average...

Inference - type 2 error

3. A soda vending machine is scheduled to ship an average of nine (9) ounces of soda per glass, with a standard deviation of one ounce (1) ounce. The machine manufacturer wishes to set the control limit so that for a sample of 36 soft drinks, 5% of the sample averages is higher than the upper control limit and 5% of the sample averages, lower than the limit of lower control
a. In what values should the control limits be programmed?
b. What is the probability that if the population average changes to 8.9, the change will not be detected?
C. What is the probability that if the population average changes to 9.3, the change will not be detected?

Expert Solution

a)

here for 5% in both tails, critical z =1.645

therefore lower control limit =9-1.645*1/√36= 8.726

upper control limit =9+1.645*1/√36= 9.274

b)

probability that if the population average changes to 8.9, the change will not be detected =0.8406

c)

probability that if the population average changes to 9.3, the change will not be detected =0.4361

orchestra answered 1 year ago

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