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

fortdefruitI

fortdefruitI

Answered question

2021-02-13

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.
(a) Suppose n=33 and p=0.21. Can we approximate the p^
distribution by a normal distribution? Why? What are the values of μp^ and σp^.?

Answer & Explanation

SkladanH

SkladanH

Skilled2021-02-14Added 80 answers

We have binomial experiment with n=33 and p=0.21
np=33(0.21)
np=6.93
nq=33(10.21)
nq=26.07
Since both the values np and ng are greater than 5, hence, we can approximate the p^ distribution by a normal distribution.
The formula for the mean of the hat p distribution is μp^=p^.
μp^=0.21
The formula for the standard error of the normal approximation to the p^ distribution is
σp^=pqn
σp^=0.21(10.21)33
σp^=0.071

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