Question 436310: A battery operated digital pressure monitor is being developed for use in calibrating pneumatic pressure gauges in the field. It is thought that 95% of the readings it gives lie within 0.01 lb/in^2 of the true reading. In a series of 100 tests, the gauge is subjected to a pressure of 10,000 lb/in^2. A test is considered to be a success if the reading lies withing 10,000 +/- lb/in^2. We want to tst Ho: p=.95 H1: p does not equal .95 at the alpha = .05 level.
A. What are the critical points for the test?
B. When the data are gathered, it is found that 98 of the 100 readings were successful. Can Ho be rejected at the alpha =.05 level? To what type error are you now subject?
THANK YOU in advance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A battery operated digital pressure monitor is being developed for use in calibrating pneumatic pressure gauges in the field.
It is thought that 95% of the readings it gives lie within 0.01 lb/in^2 of the true reading.
In a series of 100 tests, the gauge is subjected to a pressure of 10,000 lb/in^2. A test is considered to be a success if the reading lies withing 10,000 +/- (?)lb/in^2. We want to test
Ho: p=.95
H1: p does not equal .95
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at the alpha = .05 level.
A. What are the critical points for the test?
z = +/-1.96
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B. When the data are gathered, it is found that 98 of the 100 readings were successful. Can Ho be rejected at the alpha =.05 level?
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z(0.98) = (0.98-0.95)/sqrt[0.95*0.05/100] = 1.3765
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Since the test stat is not in the reject interval,
fail to reject Ho.
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By the way, the p-value = 2*P(z> 1.3765) = 2*0.0843 = 0.1686
Since the p-value is greater than 5% fail to reject Ho.
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To what type error are you now subject?
Ans: You have not reject Ho. You are subject
to a Type II error.
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Cheers,
Stan H.
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