Answer are
a) The Excepted value (p-hat) of p is 0.57
b) The Standard error of p is 0.05
c) Sampling distribution of p is Normal distribution
d) E(p-hat) = 0.57 , σ(p-hat) = 0.05
Excepted value or "p-hat" is defined as the ratio of number of succes in any sample or event to the total the size of sample . It is also known as sample proportion.
P-hat = X/ N
we have given that,
Sample size (N) = 100
Probability of an event occuring (p) or population proportion = 0.57
The Excepted value of sample proportion i.e p-hat is equal to population proportion i.e p
a) so, excepted value of p = 0.57
b) Standard error of p-hat is equal to square roots of product of p and (1-p) divided by sample size .
Standard error of p- hat = √p(1-p)/n
= √0.57 × 0.43/100= 0.05
c) Sampling distribution of sample mean is normal distribution using central limit theorem.
d) Sampling distribution of p shows
E(p-hat) = 0.57
σ(p-hat) = 0.05
Hence, we get all the required values of excepted value of p , standard error of p , distribution of p.
To learn more about Excepted value or p-hat , refer:
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