Math Is Fun Forum

corvon

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Stats question

This is a practice problem in my textbook:
In a crossover trial comparing a new drug to a standard, π denotes the probability that the new one is judged better. It is desired to estimate π and test H0: π = 0.5 vs. Ha: π ≠ 0.5. In 20 independent observations, the new drug is better each time.  Find the likelihood function. Give the maximum likelihood estimate of π.

Note:  My answer key states that the likelihood function is L(π) = π^20 and the maximum likelihood estimate of π is π^ = 1.  But how did they get this?  Any explanations would be appreciated!