- #1
safina
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Homework Statement
The number of sales made by a used car salesman, per day, is a Poisson random variable with parameter [tex]\lambda[/tex]. Given a random sample of the number of sales he made on n days, what is the most powerful test of the hypothesis Ho: p = 0.10 versus Ha: p = 0.25, where p is the probability he makes at least one sale (per day)?
Homework Equations
[tex]f\left(x;\lambda\right) = \frac{e^{-\lambda}\lambda^{x}}{x!}[/tex]
The Attempt at a Solution
I applied the single likelihood ratio test which Rejects Ho if [tex]\lambda[/tex] [tex]\leq[/tex] k which I found equivalent in saying to reject Ho if [tex]\sum Xi[/tex] [tex]\leq[/tex] k' where k' is given by [tex]P\left[\sum Xi \leq k'\right] = \alpha[/tex]
But it seems not correct since the hypotheses involve p and not the parameter [tex]\lambda[/tex]. Please help me solve this problem.