Describe the sampling distribution of p Assume the size of t

Describe the sampling distribution of p. Assume the size of the population is 30,000. n = 800, p = 0.443 Describe the shape of the sampling distribution of p. Choose the correct? Answer below. The shape of the sampling distribution of p is not normal because nLT0.05N and np(1 - p) LT 10. The shape of the sampling distribution of p is approximately normal because nLT0.05N and np(1 - p)lt 10. The shape of the sampling distribution of pis approximately normal because nLE0.05N and np(1 -p)GE10. The shape of the sampling distribution of pis not normal because nLE0.05N and np(1 -p)GE10. Determine the mean of the sampling distribution of p. mu^p = (Round to three decimal places as needed.) Determ le the standard deviation of the sampling distribution of p. sigma P (Round to three decimal places as needed.)

Solution

1.

Here,

0.05N = 0.05*30000 = 1500 > n = 800. [hence, n <=0.05N is satisfied!]

n p(1-p) = 800*0.443*(1-0.443) = 197.4008 > 10.

Hence,

OPTION C: The shape of the samplinh distribution of p^ is approximately normal because n<0.5N and np(1-p)>=10. [ANSWER]

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2.

u(p^) = 0.443 [ANSWER]

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3.

sigma(p^) = sqrt(p(1-p)/n) = sqrt(0.443*(1-0.443)/800)

= 0.017562424 [ANSWER]