SOLUTION: Find the P-value for the indicated hypothesis test. A manufacturer claims that fewer than 8% of its products are defective. In a random sample of 120 such products, 12% are defe

Question 1141673: Find the P-value for the indicated hypothesis test.
A manufacturer claims that fewer than 8% of its products are defective. In a random sample of 120 such products, 12% are defective. Find the P-value for a test to support the manufacturer's claim.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Given the assumptions of normality and randomness are present,
a one way test (fewer than 8% is one way) is a one sample proportion test with critical value z<-1.645. Note, 12% is not an integer, so one can use 14/120 as the nearest integer to 12% and 10/120 for the nearest integer to 8%. This is an important distinction in this kind of problem where exact per cents do not occur for specific numbers of people.
Here, it is done using per cents
z=(.08-.12)/sqrt(p*(1-p)/n)
=-0.04/sqrt (.08*.92/120)
=-0.04/0.0248
=-1.61
p-value is 0.0537
I suspect this is the value that is desired, but it is important to recognize that this is a discrete function here and not continuous.
Here, it is done using integers closest to the given per cents
z=(10-14)/120/sqrt (10/120)(110/120)/120
=-0.03333/0.0252
=-1.32 p-value is 0.0934
And if one wishes for an exact result, the binomial formula may be used.
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