Describe the sampling distribution of hat(p). Assume the size of the population is 25,000. n=600, p=0.4 A) Not normal because n <= 0.05 N and np(1-p) <10 B)Not normal because n <= 0.05 N and np(1-p) >= 10 C) Approximately normal because n <= 0.05 N and np(1-p) <10 D)Approximately normal because n <= 0.05 \ N and np(1-p) >= 10 Determine the mean of the sampling distribution of hat(p) mu_(hat(p))=? Determine the standard deviation of the sampling distribution of hat(p) sigma_(hat(p))=?

beefypy

beefypy

Answered question

2022-10-15

Describe the sampling distribution of p ^ . Assume the size of the population is 25,000.
n=600, p=0.4
A) Not normal because n 0.05   N and np(1-p) <10
B)Not normal because n 0.05   N and np(1-p) \geq 10
C) Approximately normal because n 0.05   N and np(1-p) <10
D) Approximately normal because n 0.05   N and n p ( 1 p ) 10
Determine the mean of the sampling distribution of p ^
μ p ^ = ?
Determine the standard deviation of the sampling distribution of p ^
σ p ^ = ?

Answer & Explanation

Kamden Simmons

Kamden Simmons

Beginner2022-10-16Added 10 answers

Since 0.05 N = 0.05 25000 = 1250 so n 0.05 N
and
Since
n p ( 1 p ) = 600 0.4 ( 1 0.4 ) = 144
So n p ( 1 p ) 10
Both conditions are met so sampling distribution of p ^ is approximately normal. So option D is correct.
μ p ^ = p = 0.4
and
σ p ^ = p ( 1 p ) n = 0.4 ( 1 0.4 ) 600 = 0.020

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