(1) Forty-nine items are randomly selected from a population of 500 items. The sample mean is
40 and the sample standard deviation 9. Develop a 99% confidence interval for the population
mean. (Round
4.5
Show that
j 1
a a
j 1
1
2
a a
1
L a j P N j ai P N i
2
i 1
L a j P N j a1 P N 1 a1 a2 P N 2 a1 a2 a3 P N 3 L
a1 P N 1 P N 2 P N 3 L
a2 P N 2 P N 3 L L
a1 P N 1 a2 P N 2 L
ai P N i
i 1
There
5.11
Let Z be a standard normal random variable and let g be a differentiable function with
derivative g .
a
Show that E g Z E Zg Z
E Zg Z
b
zg z f z dz g z f z dz E g Z
Show that E Z n 1 nE Z n
5) Explain a theoretical reason why agency size, measured as an ordinal scale of full-time
equivalent sworn staff, could be associated with the primary method for transmitting criminal
incident report
1. a Let Z have a standard normal distribution.
z2
1
exp ,
z .
2
2
z
z2
1
F z
exp
2 2 dz
2
f z
Let Y e Z Z ln Y
F Y P Y y P e Z y P Z ln y
ln y
z2
exp
2 dz
z
ln y 2 dy
1
exp
2 y
2 0
1
2. The distance from breakdown to city A has a uniform distribution over 0,200 .
There is a bus service station in city A x 0 , in city B x 200 , and in the center
of the route between A and B x 100 ,
The sufficient conditions for any estimator T to be consistent estimator for the parameter
are,
E T and Var T 0 as n .
Any estimator T is said to be an unbiased estimator for the parameter , if E T .
1. How would you define the Wilcoxon Signed Rank Test?
Wilcoxon Signed Rank Test:
Let 'e the median of the population under study with density f x .
The null and alternative hypotheses for the Wilcoxo
1. Coffee Consumption [5 points]
Coffee is a very popular beverage among Americans. Chain restaurants that are coffee only like
Starbucks or Biggby are everywhere these days. In the United States, the
Problem 1:
A rare disease exists in which only 1 in 500 are affected. A test for the disease exists
but of course it is not infallible. A correct positive result (patient actually has the disease)
occ
Assignment 1
1. Below we list several variables. Which of these variables are quantitative and which are
qualitative? Explain.
a. The dollar amount on an accounts receivable invoice.
b. The net profit