Working with sampling distribution and probability.

A southern state has an unemployment rate of 6%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

a) If the true unemployment rate is 6%, describe the sampling distribution of p^.

b) Find P(p^ >= 0.05)

c) Assume the population proposal, p, is unknown. Describe the sampling distribution of p^ based on the most recent sample.

d) Find the probability that the sample proportion will lie within 0.05 of the true proportion of people who are unemployed.

Solution Preview

a) If the true unemployment rate is 6%, then let X be the number of people who were unemployed. Obviously,
X~b(700,0.06), that is a binomial distribution with n=700, and p=0.06. So p^=(X1+X2+...+X700)/700 approximately follows normal distribution, where
<br> E(p^)={E(X1)+E(X2)+...+E(X700)}/700=0.06,
<br>and
<br> ...

Solution Summary

A southern state has an unemployment rate of 6%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

a) If the true unemployment rate is 6%, describe the sampling distribution of p^.

b) Find P(p^ >= 0.05)

c) Assume the population proposal, p, is unknown. Describe the sampling distribution of p^ based on the most recent sample.

d) Find the probability that the sample proportion will lie within 0.05 of the true proportion of people who are unemployed.

Suppose the annual consumption of chicken mean is 20.84 pounds per person, and that the standard deviation for the consumption of chicken per person is 9.193 pounds. The mean weight of chicken consumed for a sample of 200 randomly selected people is one value of many that form the samplingdistribution of sample means.
Descri

6.30
Given a population in which the proportion of items with a desired attribute is p=0.25, if a sample of 400 is taken:
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P?
b. What is the probability the propo

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B. The standard deviation of the samplingdistribution is always "o"
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D. All of the above

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Suppose the annual consumption of chicken mean is 20.84 pounds per person and that the standard deviation for the consumption of chicken per person is 9.193 pounds. The mean weight of chicken consumed for a sample of 200 randomly selected people is one value of many that form the samplingdistribution of sample means.
Descri

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