SOLUTION: A manufacturer of a patent medicine claims that it is 90% effective in relieving an allergy for a period of 8 hours. 200 people that had an allergy were sampled and it was found th

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Question 894907: A manufacturer of a patent medicine claims that it is 90% effective in relieving an allergy for a period of 8 hours. 200 people that had an allergy were sampled and it was found that only 160 people received relief. Is the manufacture's claim legitimate?
assume a=0.01
Answer by stanbon(75887) About Me  (Show Source):
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A manufacturer of a patent medicine claims that it is 90% effective in relieving an allergy for a period of 8 hours. 200 people that had an allergy were sampled and it was found that only 160 people received relief. Is the manufacture's claim legitimate?
Ho: p = 0.9 (claim)
Ha: p < 0.9
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x-bar = 160/200 = 0.8
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z(0.8) = (0.8-0.9)/sqrt[0.9*0.1/200} = -4.715
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p-value = P(z < -4.715) = 0.00000121...
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Since the p-value is less than 1%, reject Ho.
The manufacturer's claim is not supported by the test results.
Cheers,
Stan H.