Describe the sampling distribution of p. Assume the size of the population is 20,000.n 800, p 0.356Describe the shape of the sampling distribution of p. Choose the correct answer below.A.The shape of the sampling distribution of p is not normal because n s 0.05N and np(1 - p)< 10В.The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p) 10AС.The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p)2 10D.The shape of the sampling distribution of p is not normal because ns 0.05N and np(1 -p)z 10.Determine the mean of the sampling distribution of p.(Round to three decimal places as needed.)HAрDetermine the standard deviation of the sampling distribution of p.(Round to three decimal places as needed.)р

Question
Asked Oct 21, 2019
Describe the sampling distribution of p. Assume the size of the population is 20,000.
n 800, p 0.356
Describe the shape of the sampling distribution of p. Choose the correct answer below.
A.
The shape of the sampling distribution of p is not normal because n s 0.05N and np(1 - p)< 10
В.
The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p) 10
A
С.
The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p)2 10
D.
The shape of the sampling distribution of p is not normal because ns 0.05N and np(1 -p)z 10.
Determine the mean of the sampling distribution of p.
(Round to three decimal places as needed.)
HA
р
Determine the standard deviation of the sampling distribution of p.
(Round to three decimal places as needed.)
р
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Describe the sampling distribution of p. Assume the size of the population is 20,000. n 800, p 0.356 Describe the shape of the sampling distribution of p. Choose the correct answer below. A. The shape of the sampling distribution of p is not normal because n s 0.05N and np(1 - p)< 10 В. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p) 10 A С. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p)2 10 D. The shape of the sampling distribution of p is not normal because ns 0.05N and np(1 -p)z 10. Determine the mean of the sampling distribution of p. (Round to three decimal places as needed.) HA р Determine the standard deviation of the sampling distribution of p. (Round to three decimal places as needed.) р

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Expert Answer

Step 1

The provided information is as follows:

Size of population (N)= 20000
Sample size(n) 800
Probability (p) 03 56
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Size of population (N)= 20000 Sample size(n) 800 Probability (p) 03 56

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Step 2

According to the central limit theorem, the normal approximation is not accurate for small values of n so it is better to use normal approximation only if n ≤ 0.05N and np (1-p) > 10.

0.05x N 0.05x 20000
1000
n(800)
np(1-p) 800x 0.356 x 0.644
183.41
>10
Therefore, option C is correct
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0.05x N 0.05x 20000 1000 n(800) np(1-p) 800x 0.356 x 0.644 183.41 >10 Therefore, option C is correct

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Step 3

According to the central limit theorem, sample proportion that is p̂ is normally distributed wit...

=0.356
Therefore, the required mean is 0.356
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=0.356 Therefore, the required mean is 0.356

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