Let Y1Y2 Yn be independent and identically distributed rando

Let Y1,Y2,.. Yn be independent and identically distributed random variables with discrete probability function given by (Bernoulli Distribution) Derive the likelihood function L(p). Find the most powerful test for testing Ho: p = po versus Ha : p = pa, where pa > po. Show that your test specifies that Ho be rejected for certain values of y2. How do you determine the value of k so that the test has significance level alpha ? You need not do the actual computation. A clear description of how to determine k is adequate. In the test derived in parts (l)-(3) uniformly most powerful for testing H0 : P = Po vs Ha : P > Po? Why or why not?

Solution

The test derived is not necessarily the most powerful method of testing. We are using a normal approximation in this case, which may not be true for small values on n. In such scenarios, we use methods like bootstrapping, which are generally more accurate in case of smaller values of n.