(Example 3) Income in Maryland According to a 2018 Money magazine article, Maryland has one of the highest per capita incomes in the United States, with an average income of $75,847 . Suppose the standard deviation is $ 32 , 000 and the distribution is right-skewed. A random sample of 100 Maryland residents is taken. a. Is the sample size large enough to use the Central Limit Theorem for means? Explain. b. What would the mean and standard error for the sampling distribution? c. What is the probability that the sample mean will be more than $ 32 , 000 away from the population mean?
(Example 3) Income in Maryland According to a 2018 Money magazine article, Maryland has one of the highest per capita incomes in the United States, with an average income of $75,847 . Suppose the standard deviation is $ 32 , 000 and the distribution is right-skewed. A random sample of 100 Maryland residents is taken. a. Is the sample size large enough to use the Central Limit Theorem for means? Explain. b. What would the mean and standard error for the sampling distribution? c. What is the probability that the sample mean will be more than $ 32 , 000 away from the population mean?
Solution Summary: The author analyzes whether the sample size is large enough to use the central limit theorem.
(Example 3) Income in Maryland According to a 2018 Money magazine article, Maryland has one of the highest per capita incomes in the United States, with an average income of
$75,847
. Suppose the standard deviation is
$
32
,
000
and the distribution is right-skewed. A random sample of 100 Maryland residents is taken.
a. Is the sample size large enough to use the Central Limit Theorem for means? Explain.
b. What would the mean and standard error for the sampling distribution?
c. What is the probability that the sample mean will be more than
$
32
,
000
away from the population mean?
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
2 (VaR and ES) Suppose X1
are independent. Prove that
~
Unif[-0.5, 0.5] and X2
VaRa (X1X2) < VaRa(X1) + VaRa (X2).
~
Unif[-0.5, 0.5]
8 (Correlation and Diversification)
Assume we have two stocks, A and B, show that a particular combination
of the two stocks produce a risk-free portfolio when the correlation between
the return of A and B is -1.
9 (Portfolio allocation)
Suppose R₁ and R2 are returns of 2 assets and with expected return and
variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find
−∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest
risk.
Chapter 9 Solutions
The King's minion: Richelieu, Louis XIII, and the affair of Cinq-Mars
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