Homework 2 - 550.430 Introduction to Statistics Spring 2010...

550.430 Introduction to Statistics
Spring 2010
Naiman
Homework #2
Due Monday Feb 13th
(1) Chapter 7 #24
(2) Chapter 7 #35
(3) Chapter 7 #37
(4) Suppose we estimate the mean income μ for people living in some city using an esti-
mator ˆ μ with the property that
ˆ μ ∼ N ( μ, σ
2
) .
(a) What is the probability that ˆ μ < μ + . 75 σ ?
(b) What is the probability that ˆ μ > μ + 1 . 25 σ ?
(c) What is the probability that μ + . 60 σ < ˆ μ < μ + . 75 σ ?
(d) What is the probability that μ - . 60 σ < ˆ μ < μ + . 75 σ ?
(e) What is the probability that | ˆ μ - μ | < σ ?
(5) Suppose we estimate the mean height of μ for people living in some city using an
estimator ˆ μ. We also estimate the standard deviation σ
ˆ μ
of the estimator using an
estimator denoted by s
ˆ μ
. Assume that the quantity
ˆ μ - μ
s
ˆ μ
is distributed as Student’s t with 10 degrees of freedom.
(a) What is the probability that ˆ μ > μ + 1 . 812 s
ˆ μ
?
(b) What is the probability that | ˆ μ - μ | < 1 . 812 s
ˆ μ
(6) (Use of Chebychev’s inequality) Consider estimation of a population mean μ whose