STAT 409
Examples for 10/10/2011 (2)
Fall 2011
1.
The overall standard deviation of the diameters of the ball bearings is = 0.005 mm. The overall mean diameter of the ball bearings must be 4.300 mm. A sample of 81 ball bearings had a sample mean diameter
STAT 409 Fall 2011 Version A
Name Quiz 3
(10 points)
ANSWERS
.
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
In a random sample of 120 male customers at Burger Queen, 84 ordered
STAT 409
Fall 2011
Homework #7
(due Friday, October 21, by 4:00 p.m.)
1.
A researcher wishes to determine whether the starting salaries of high-school math
teachers in private schools are higher than those of high-school math teachers in
public schools. S
STAT 409
Homework #5
( due Friday, October 7, by 4:00 p.m. )
Fall 2011
1.
Consider Gamma ( , = "usual " ) distribution. That is,
f ( x; , ) =
Suppose is known. a)
1 ( )
x -1 e - x
,
0 < x < .
Determine the Fisher information I ( ).
ln f ( x; ) = - ln ( )
STAT 409
Homework #4
( due Friday, September 23, by 4:00 p.m. )
Fall 2011
1.
A random sample of 9 adult elephants had the sample mean weight of 12,240 pounds and the sample standard deviation of 450 pounds. A random sample of 16 adult hippos had the sampl
STAT 409
Fall 2011
Homework #6
( due Friday, October 14, by 4:00 p.m. )
1.
In the past, only 30% of the people in a large city felt that its mass transit system is
adequate. After some changes to the mass transit system were made, we wish to test
if the p
STAT 409
Fall 2011
Name
ANSWERS
.
Version A
Quiz 6
(10 points)
Be sure to show all your work, your partial credit might depend on it.
No credit will be given without supporting work.
1.
H 0 : m X = m Y vs. H 1 : m X > m Y
We wish to test
based on n 1 = 8
STAT 409
1.
Fall 2011
Examples for 11/07/2011
A group of 500 children (250 boys and 250 girls) were asked to identify their
favorite color. We obtain the following data:
Favorite Color
Sex
Yellow
Red
Blue
Brown
Boys
107
85
33
25
Girls
93
65
67
25
A toy ma
STAT 409
1.
Fall 2011
Examples for 11/09/2011
The following is a random sample from a certain population:
24
19
17
12
20
11
22
15
22
26
18
We wish to test H 0 : m = 17 vs. H 1 : m > 17, where m is the population
median.
a)
Use the sign test. What is the p
STAT 409
Examples for 11/14/2011
Fall 2011
A pharmaceutical company is planning to introduce a new painkiller. In a preliminary
experiment to determine effectiveness, 30 people were randomly selected, of whom 15 were
given the new painkiller and 15 were g
1.
Let X 1 , X 2 , , X n be a random sample of size n = 19 from the normal
distribution N ( , 2 ).
a)
Find a rejection region of size = 0.05 for testing
H 0 : 2 = 30 vs. H 1 : 2 > 30.
For which values of the sample variance s 2 should the null hypothesis
Practice Problems for 8.1
1.
Crosses of mice will produce either black, brown, or albino offspring. Mendels
model predicts that the probability of a black offspring is 9/16 ; the probability
of a brown offspring is 3/16 ; and the probability of an albino
STAT 409
1.
Let X 1 , X 2 , , X n be a random sample of size
probability density function
f X (x) = f X ( x ; ) = ( 1 ) 2
a)
Fall 2011
Examples for 11/02/2011 (2)
ln x
x
n
from the distribution with
x > 1,
,
> 1.
Find the form of the uniformly most powe
STAT 409
Examples for 11/02/2011 (1)
Fall 2011
1.
The developers of a math proficiency exam to be used at Anytown State University
believe that 60% of all incoming freshmen will be able to pass the exam. In a random
sample of 200 incoming freshmen, 105 pa
STAT 409
1.
Fall 2011
Examples for 10/31/2011
Alex buys a package of Sour Jelly Beans. On the package, it says that 50% of all
jelly beans are lemon, 30% are cherry, and 20% are lime. When Alex opens the
package, he finds 15 lemon, 9 cherry and 12 lime je
STAT 409
Fall 2011
Examples for 10/28/2011
Example 1:
1
2
3
4
5
p0(x )
0.25
0.15
0.20
0.05
0.35
p1(x )
0.20
0.20
0.20
0.20
0.20
H 0 : X has p.m.f. p 0 ( x )
vs.
H 1 : X has p.m.f. p 1 ( x ).
1
(x)
2
3
4
5
1.25
0.75
1
0.25
1.75
Reject H 0 if x = 4
= 0.05,
STAT 409
Fall 2011
Examples for 10/26/2011
Consider a family of probability distributions with a p.d.f. of the
form
f ( x ; ) = x 1, 0 < x < 1, zero elsewhere, 1.
To test the simple hypothesis H 0 : = 1 against the alternative
simple hypothesis H 1 : = 1,
STAT 409
Fall 2011
Examples for 10/24/2011
H0: = 0
vs.
H 1 : = 1.
Likelihood Ratio:
( x 1 , x 2 ,., x n ) =
L ( 0 ; x 1 , x 2 ,., x n )
.
L ( 1 ; x 1 , x 2 ,., x n )
Neyman-Pearson Theorem:
C = cfw_ ( x 1 , x 2 , , x n ) : ( x 1 , x 2 ,., x n ) k .
( Rej
STAT 409
Fall 2011
Examples for 10/21/2011
H0: = 0
H 1 : = 1.
vs.
Likelihood Ratio:
( x 1 , x 2 ,., x n ) =
L ( 0 ; x 1 , x 2 ,., x n )
.
L ( 1 ; x 1 , x 2 ,., x n )
Neyman-Pearson Theorem:
C = cfw_ ( x 1 , x 2 , , x n ) : ( x 1 , x 2 ,., x n ) k .
( Rej
STAT 409
Fall 2011
Examples for 10/19/2011
Let X 1 , X 2 , , X 16 be a random sample of size n = 16 from a N ( , 2 )
distribution. We are interested in testing H 0 : = 39 vs. H 1 : > 39.
1.
Recall: If X 1 , X 2 , , X n are i.i.d. N ( , 2 ), then
( n 1 ) S
STAT 409
2.
Fall 2011
Examples for 10/17/2011
Suppose n = 49 observations are taken from a normal distribution where = 8.0
for the purpose of testing H 0 : = 60 versus H 1 : > 60.
a)
What is the significance level associated with the rejection region
Reje
STAT 409
Fall 2010
Name
ANSWERS
.
Version A
Quiz 5
(10 points)
Be sure to show all your work, your partial credit might depend on it.
No credit will be given without supporting work.
1.
A travel agent randomly sampled individuals in her target market to d
STAT 409
Fall 2010
Name
ANSWERS
.
Version B
Quiz 5
(10 points)
Be sure to show all your work, your partial credit might depend on it.
No credit will be given without supporting work.
1.
A travel agent randomly sampled individuals in her target market to d
STAT 409
Fall 2011
Homework #11
(due Friday, December 2, by 4:00 p.m.)
From the textbook:
8.7-1 (
8th edition (
)
)
D = 0.40 < 0.45
Do NOT Reject H 0 at = 0.20.
at x = 0.40-
an 80% confidence band for F ( x ) is included ( note the CDF of U ( 0, 1 ) is in
STAT 409
Fall 2011
Extra Credit
(3 points)
1.
The Red Army Manual states that the overall average weight of the Red Army
soldiers must be 85 kg. A Red Army general wishes to test whether the overall
average is as is specified by the Manual. That is, he wi
STAT 409
1.
Fall 2011
Examples for 11/28/2011 (2)
A statistics instructor teaches two statistics classes, one in the morning and one
in the afternoon. Suppose the probability that the instructor gives a good morning
lecture is 0.3. If the morning lecture
STAT 409
Fall 2011
Examples for 11/28/2011
Let X 1 , X 2 , , X n be a random sample from a continuous-type population.
Let Y 1 < Y 2 < < Y n denote the corresponding order statistics.
P ( Y i < p < Y j ) = P ( i [ number of observations to the left of p ]