Describe the sampling distribution of p hat. Assume the size of the population i

Question

Describe the sampling distribution of p hat. Assume the size of the population is .
n=300, p=0.1

1. Choose the proase that best describes the shape of the sampling distributin of p hat

A) Approximately normal because n0.05N and np(1 - p) < 10.

B) Not normal because n 0.05N and (1 - p) < 10.

C) Not normal because n 0.05N and np(1 - p)greater than or equals 10.

D) Approximately normal because n0.05N and np(1 - p) greater than or equals 10.

2. Determine the mean of the samping distribution of p hat

3. Determine the standard deviation of the sampling distribution of p hat

Explanation / Answer

sol:

n=300 large sample

np=300*0.1=30

n(1-p)=300(1-0.1)=0.9*300=270

D) Approximately normal because n0.05N and np(1 - p) greater than or equals 10.

sampling distribution is normal

2. Determine the mean of the samping distribution of p hat

p hat=p=0.1

3.Determine the standard deviation of the sampling distribution of p hat

phat=sqrt[p(1-p)/n]

=sqrt[0.1(1-0.1)/300]

=0.017

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