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Course: VHM 801, Fall 2009School: UPenn
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6.52 ------------- A Exercise farmer "recognizes" water in 4 trials out of 5. (a) The hypothesis of interest is H0: p=0.5 against the alternative Ha: p>0.5. (It is difficult to imagine that p<0.5, unless there is some error in the experiment or the farmer messes up.) (b) Assuming independence between trials, and same probability p of getting it right (water or not), this is a...
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6.52
-------------
A Exercise farmer "recognizes" water in 4 trials out of 5.
(a) The hypothesis of interest is H0: p=0.5 against the alternative
Ha: p>0.5. (It is difficult to imagine that p<0.5, unless there is some
error in the experiment or the farmer messes up.)
(b) Assuming independence between trials, and same probability p
of getting it right (water or not), this is a binomial setting.
Therefore X = number of correct answers B(5,p), follows in particular
B(5,0.5) if the farmer is guessing.
(c) Observed value x=4. The test statistic is simply X. Critical values
are large (larger than the expected value 2.5 under H0).
Therefore, P-value = P(X>=4) = P(X=4) + P(X=5)
= 5...
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