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Variance, estimator for mean, millionaire net worth

#1
Suppose you are sampling from a population with mean µ = 1,065 and standard deviation σ = 500. The sample size is n = 100. What are the expected value and the variance of the sample mean X? Show and explain your work (study guide # 5-41).

#2
Suppose a new estimator for the population mean is discovered. The new estimator is unbiased and has a variance equal to σ^2 / n^2 . Discuss the merits of the new estimator compared with the sample mean. Show and work and explain your answer (study guide # 5-65).

#3
Thomas Stanley, who surveyed 200 millionaires in the United States for his book The Millionaire Mind, found that those in that bracket had an average net worth of $9.2 million. The sample variance was 1.3 million $^2. Assuming that the surveyed subjects are a random sample of U.S. millionaires, give a 99% confidence interval for the average net worth of U.S. millionaires. Show and explain your work (study guide # 6-68).

#4
Use the following random sample of suitcase prices to construct a 90% confidence interval for the average suitcase price. Show and explain your answer (study guide # 6-84).
$285, $110, $495, $119, $125, $250, $320

Solution Preview

Four (4) Intro to Stats Problems
Please show all work and explain so I can compare to my work in order for me to find where I may be messing up. I am having trouble with variance so please be specific in this case. I really need to understand the concept, so please explain well.

#1
Suppose you are sampling from a population with mean µ = 1,065 and standard deviation σ = 500. The sample size is n = 100. What are the expected value and the variance of the sample mean X? Show and explain your work (study guide # 5-41).

Answer
From central limit theorem
Expected value of sample mean = Population mean = 1065
Variance of sample mean = =500/10 =50

#2
Suppose a new estimator for the population mean is discovered. The new estimator is unbiased and has a variance equal ...

Solution Summary

Variance, estimator for mean and a millionaires net worth is examined.

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