Supplementary exercise 6.68 of IPS7e
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A 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 follows B(5,p), 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*0.5^4*(1-0.5) + 0.5^5 = 0.1875
This probability could also have been obtained from Table 1 of Stephens. 
It shows that the outcome x=4 is not significant at the 5%- or 10%-level.

Conclusion: There is no convincing evidence that the farmer does better
than pure guessing.

You will have noted that the model and testing procedure is identical to the
taste testing example from Lecture 5.