HW 2: Due Tuesday, January 19th
More on likelihood ratio test methods for deriving test statistics and t-tests.
1. 10.11 (pg. 554): 10.105
Suppose Y1 , Y2 , . . . , Yn N (, 2 ). Both and 2 are unknown.
2
2
H0 : 2 = 0 vs. Ha : 2 > 0
The LRT methods says to

PSTAT 120C Spring 2015
Midterm Examination Solution
1. [10 points] Two methods, A and B, were used in a determination of the latent heat of
fusion of ice. The investigators wanted to find out by how much the methods differed. The
following table gives the

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PSTAT 120C
Probability and Statistics
Assignment 1
1. An auditor wants to estimate the mean value of all accounts receivable. It is known
that the population of accounts receivable is normal with standard deviation 43. A
sample of size 36 was taken from t

PSTAT 120C
Probability and Statistics
Exercise set 1
1. The diameter of the ball used for a particular sport should be 5 cm. A sample of
size 20 was taken and diameters are measured. The sample mean was found to be 4.9
cm and the population standard devia

PSTAT 120C
Probability and Statistics
Exercise set 1 Solution
1. (a) H0 : = 5 vs. H1 : < 5.
The z-statistic is given by z =
4.95
0.25
20
= 1.789 which is to be compared to
z.05 = 1.645. As the z value is smaller than the critical value, we reject the
null

PSTAT 120C
Probability and Statistics
Exercise set 2
1. Suppose that Y is a random sample of size 1 from a population with density
f (y | ) =
y 1 , 0 y 1
0,
elsewhere.
where > 0.
(a) Sketch the power function of the test with the critical region Y > .5.
(

PSTAT 120C
Probability and Statistics
Assignment 2
1. Suppose that we have 9 independent observations from a normal distribution with
standard deviation 10. We wish to test
H0 : = 150 vs. H1 : = 150
The likelihood ratio test with level = 0.05 has the crit

University of California, Santa Barbara
PSTAT 120C: Probability and Statistics
Spring 2015
Instructor: Vasudevan Mangalam
Oce Hrs: MT 11:00-12:00
Lectures: TR 12:30-1:45 NH 1006
Oce: South Hall 5519
Email: [email protected]
TA information:
Time
T 5:

PSTAT 120C
PROBABILITY AND STATISTICS
Vasudevan Mangalam
Department of Statistics and Applied Probability
University of California, Santa Barbara
Contents
1 Testing Statistical Hypotheses
1.1 The Null and Alternative Hypotheses . . . . . . . . . . . . . .

HW 3: Due Tuesday, January 26th
T-test and nonparametric.
1. 10.8 (pg. 529) 10.73. For parts a) and b) nd the exact p-value and also make
decision via RR method.
a) H0 : RR RC = 0 vs. Ha : RR RC = 0 for = 0.05
> (sp = sqrt(9*(3.92^2 + 3.98^2)/(18)
[1] 3.9

HW 1: Due Tuesday, January 12th
An introduction to hypothesis testing and likelihood ratio test methods for deriving
test statistics. Enjoy. Note: problems 3 and 4 will not be submitted, they are for fun.
1. 10.2 (pg. 494):
10.2: Note: Y Bin(n = 20, p)
H0

PSTAT 120C:
Equal Probability Tests
February 21, 2017
2 goodness of fit tests
Degrees of freedom
Fitting parameters
Survey Example
1. We survey 800 people and ask them if they have a favorable or unfavorable view of their
senator.
2. Our data finds 365

PSTAT 120C:
Final Exam Information
Tuesday, March 21. 8:0011:00AM
The policies for the final will be essentially the same as they were for the midterm.
Please arrive early so that we can get started on time.
You will have 3 hours to complete the exam.

PSTAT 120C:
Midterm Information and Practice Questions
Exam on February 14, 2017
The midterm exam is on Tuesday during lecture.
Please be sure to bring
? One formula sheet (you may write on two sides of one piece of 8.5 by 11 paper).
? Calculator, and
?

PSTAT 120C:
Solutions to Assignment # 3
February 8, 2017
1. There is actually a better way to look at the data from last week. The data was taken from
the same counties each year.
County
2015
2016
Dierence
5.9822
5.8949
6.7690
8.2101
7.8076
7.2107
7.2501

PSTAT 120C:
Assignment 3
Due February 1, 2017
These problems will be due in lecture next Thursday.
1. There is actually a better way to look at the data from last week. The data was taken from
the same counties each year.
County
Humboldt County, CA
Imperi

PSTAT 120C:
Assignment 2
Due January 26, 2017
These problems will be due in lecture next Thursday.
1. Suppose that we have n independent observations x1 , . . . , xn from a normal distribution with
mean and variance 2 , and we want to test
H0 :
2
=1
H1 :

PSTAT 120C:
Assignment #4
Due February 9, 2017
Please turn in Assignments in Lecture next Thursday.
1. In a 1993 study from the British Medical Journal, the researchers compared the number of
emergency room visits due to car accidents on Friday the 6th an

PSTAT 120C:
Assignment #5
Due February 23, 2017
Please turn in Assignments in Lecture next Thursday.
1. The following data on the number of incident reports filed at two police stations was collected
over a number of weeks.
Station 1
Station 2
43
71
38
9

PSTAT 120C:
Practice Questions
Midterm on February 14, 2017
The midterm exam is next Tuesday during lecture.
Here are the solutions to the practice questions.
1. (a) When we talk about power in this course we are referring to the probability of rejecting

PSTAT 120C:
Assignment 1
Due January 19, 2017
These problems will be due in lecture next Thursday.
1. Suppose that we have 9 independent observations from a normal distribution with standard
deviation 10. We wish to test
H0 : = 150 vs. HA : 6= 150
The GLR

PSTAT 120C:
Assignment 2
Due January 26, 2017
These problems will be due in lecture next Thursday.
1. Suppose that we have n independent observations x1 , . . . , xn from a normal distribution with
mean and variance 2 , and we want to test
H0 :
2
=1
H1 :

PSTAT 120C:
Assignment 3
Due February 1, 2017
These problems will be due in lecture next Thursday.
1. There is actually a better way to look at the data from last week. The data was taken from
the same counties each year.
County
Humboldt County, CA
Imperi

PSTAT 120C:
Midterm Information and Practice Questions
Exam on February 14, 2017
The midterm exam is on Tuesday during lecture.
Please be sure to bring
? One formula sheet (you may write on two sides of one piece of 8.5 by 11 paper).
? Calculator, and
?

PSTAT 120C:
Prior Distributions
March 9, 2017
1. Prior Information
2. Binomial model with a Beta prior
3. Poisson model with a Gamma prior
The Bayesian Philosophy
Unknowns are random variables
The parameters are now random variables
Information is desc

Take your time in explaining how we use NPL to get the test, then how we use alpha to
nd the actual form of RR. We will also cover a LRT test example, this will be dicult for
students. Muahahahaha. Muhahahaha. Its important that we cover all of what is li

PSTAT 120C:
Assignment 1
Due January 19, 2017
These problems will be due in lecture next Thursday.
1. Suppose that we have 9 independent observations from a normal distribution with standard
deviation 10. We wish to test
H0 : = 150 vs. HA : 6= 150
The GLR

PSTAT 120C:
Wilcoxon Signed-Rank Test
February 2, 2017
1. Incorporating more information into the sign test
2. Signed-Rank Test
3. Distribution of the test statistic
4. Ties
Sign Test
H0 : x = y
Look at Xi Yi
Count how many are positive (as opposed to

PSTAT 174/274 Winter 2017: Homework 4
Abbreviations:
BD refers to Introduction to Time Series and Forecasting by Brockwell and Davis, second
edition. LN refers to class Lecture Notes.
1. Review Appendix B of [BD]. (Posted on Gaucho Space)
2. Suppose that

PSTAT 120C:
Assignment #5
Due February 23, 2017
Please turn in Assignments in Lecture next Thursday.
1. The following data on the number of incident reports filed at two police stations was collected
over a number of weeks.
Station 1
Station 2
43
71
38
9