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Chapter 5: Q37E (page 320)

Suppose a random sample of n = 500 measurements is selected from a binomial population with probability of success p. For each of the following values of p, give the mean and standard deviation of the sampling distribution of the sample proportion,p^.

  1. p= .1
  2. p= .5
  3. p= .7

Short Answer

Expert verified

The mean and standard deviation of the sampling distribution of the sampling proportion are,

  1. If p=0.1, mean = 0.1, standard deviation = 0.0134
  2. If p=0.5, mean = 0.5, standard deviation = 0.0223
  3. If p=0.7, mean = 0.7, standard deviation = 0.0204

Step by step solution

01

Given information

There is a random sample of n=500 from a binomial distribution with a probability of success p.

02

Calculate the mean and standard deviation when p=.1

The mean of the sampling distribution is equal to the true binomial proportion. So, and the standard deviation of the sampling distribution is 蟽p^=p(1-p)/n.

Therefore,

a.

If p=0.1 then, Mean Ep^=p=0.1.

Standard deviation蟽p^=0.11-0.1/500=0.0134

03

Calculate the mean and standard deviation p=.5

b.

If p=0.5 then, MeanEp^=p=0.5

Standard deviation蟽p^=0.51-0.5/500=0.0223

04

Calculate the mean and standard deviation p=.7

c.

If,p=0.7 then, MeanEp^=p=0.7

Standard deviation蟽p^=0.71-0.7/500=0.0204

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