Basic Computation:hat{p} Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that i

UkusakazaL 2020-11-05 Answered
Basic Computation:p^ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(c) Suppose n=48 and p=0.15. Can we approximate the p^ distribution by a normal distribution? Why? What are the values of μhatp and σp.?
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Layton
Answered 2020-11-06 Author has 89 answers

We have binomial experiment with n=48 and p=0.15
np=48(0.15)
np=7.2
nq=48(10.15)
nq=40.8
Since both the values np and nq are greater than 5, hence, we can approximate the hat p distribution by a normal distribution.
The formula for the mean of the p^ distribution is μhatp=p^.
μhatp=0.15
The formula for the standard error of the normal approximation to the p^ distribution is
σp^=pqn
σp^=0.15(10.15)48
σp^=0.052

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