describe the sampling distribution of pSolutionthe sampling

describe the sampling distribution of p^

Solution

the sampling distribution of P hat is approximately normal [with mean p and standard deviation sqrt of p(1-p)/n] PROVIDED that np and n(1-p) are greater than 5

We express this sampling distribution explained above as:

z = P(hat)-p/(sqrt of [p(1-p)/n])

In this case np = 200 (500*0.4)
and
n(1-p) = 300 (500*(1-0.4))

So np and n(1-p) are both > 5; therefore the sampling distribution of P(hat) can be described as approximately normal and expressed as:

P(hat)-p/(sqrt of [p(1-p)/n])

No need to use a calculator to do this; just remember the np and n(1-p) must be greater than 1 and the test statistic for p and you can answer it my testing those