Obtain the sampling distribution of overline{p}

Cheyanne Leigh 2021-02-09 Answered
Obtain the sampling distribution of p
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Expert Answer

mhalmantus
Answered 2021-02-10 Author has 106 answers

It is given that is the sample proportion of entrepreneurs whose first startup was at 30 years or more is p=0.45 and the sample size n=200
The sampling distribution of the proportion is approximately normal if np5 and n(lp)5.
Verify the conditions:
np=200×0.45
=905.
n(1p)=200×(10.45)
And
=1105
The conditions are satisfied. Therefore, the sampling distribution of the proportion is normal.
The mean of the p is E(p)=p and standard deviation of p is σp,=p(1p)n
Mean and standard deviation are calculated as below
E(p)=p=0.45
σp=p(1p)=0.45×0.55200=0.0352
Py 0.45×0.55
Thus, the sampling distribution of the proportion J of entrepreneurs whose first startup was at 30 years or more is normal with mean E(p)=0.45 and standard deviation σp,=0.0352

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