SOLUTION: Historical data show that 4% of the components produced by a certain manufacturer are defective.Someone challenged the figure of 4% and the management wanted to test whether this c

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Question 463276: Historical data show that 4% of the components produced by a certain manufacturer are defective.Someone challenged the figure of 4% and the management wanted to test whether this claim has to be modified. If a random sample of 500 items resulted in 16 defective ones, is this significant evidence that the claim is incorrect?
By considering a significance level alpha = 0.05, what is the lowest rate of defective components that the manufacturer can claim, with the same experimental test results?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
H[o]:.04n=defective.
H[a]:.04n<>defective.
.
mu=p%5Bo%5D=.04, q=.96
sigma=sqrt%28pq%2Fn%29=sqrt%28.04%2A.96%2F500%29=.00876
P=16%2F500=.032
z=%28P-p%5Bo%5D%29%2Fsigma=%28.032-.04%29%2F.00876=+-0.913%29
Since -0.913 is more than -1.96. This is not significant evidence that the claim is incorrect.
.
(x-.04)/.00876=-1.96
x-.04=-.0172
x=.0228 the lowest rate of defective components that the manufacturer can claim, with the same experimental test results.
.
Ed