Western University (Ontario)  Also known as University of Western Ontario
STATS 2857

Fall 2013
STAT 2857 Assignment 3
Problem 1. Let X be a continuous nonnegative random variable with density function f , and let
Y := X n . Find fY , the probability density function of Y .
Problem 2. A system consisting of one original unit plus a spare can functi
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
Correlation and Regression
A response variable measures an outcome of a study
o Dependent variables
An explanatory variable may explain or influence changes in a response variable
o Independent variables
Easiest to identify explanatory and response variab
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
OneWay ANOVA and posthoc tests
The weakness of doing multiple ttests is that we get multiple Pvalues, one for each test
performed
o Doesnt tell us how likely it is that the sample means are spread apart as far as these are
o The problem gets worse as
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
Confidence Intervals for p
Our discussion of statistical inference up to this point has concerned making inferences about
population means
o Now we turn to questions about the proportion of some outcome in a population when
studying a categorical variable
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
Sampling Distributions
The distribution of data from a random sample is likely to reflect the true distribution of the
population
Statistical inference is when we use information from a sample to infer something about a wider
population
o Because the resu
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
Normal Distribution
Normal curves are density curves that are symmetric, singlepeaked, and bell shaped
o Describes normal distributions
o All normal distributions have the same overall shape
o The exact density curve for a particular normal distribution
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
Binomial Distribution
The distribution of a count depends on how the data are produced
The binomial setting is as follows:
o There are a fixed number n of observation
o The n observations are all independent which means that knowing the result of one
obse
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
Probability and Random Variables
Random samples eliminate bias from the act of choosing a sample, but they can still be wrong
because of the variability that results when we choose at random
o If the variation when we take repeat samples from the same pop
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
Sampling Design
The individuals studied in an experiment are often called subjects when they are people, and
experimental units otherwise
o Explanatory variables in an experiment are often called factors
o A treatment is any specific experimental conditio
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
Hypothesis Tests for p and mu and Paired Sample Inference
We now turn to tests of significance and will assume that the conditions for inference we
described earlier are met
o When the null hypothesis H 0 : p= p0 is true, the sampling distribution of the
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
TwoSample Inference
Comparing two populations or two treatments is one of the most common situations
encountered in statistical practice
o The goal of inference is to compare the responses to two treatments or to compare the
characteristics of two popula
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
Confidence Intervals for
The National Health and Nutrition Examination Survey reports the weights and heights of
Americans every few years
o Every survey is based on a nationwide probability sample of the U.S. civilian noninstitutionalized population
o Wh
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
Descriptive Statistics
Any set of data contains information about some group of individuals
o The information is organized in variables
o The techniques of descriptive statistics apply equally to data sets obtained from a given
population or from only tho
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244

Fall 2016
Samples and Observational Studies (Chapter 7)
We collect data in order to understand phenomena or answer scientific questions
o Two approaches for collection data
One approach is the observational study is where the subject of scientific inquiry is distur
Western University (Ontario)  Also known as University of Western Ontario
STATS 3657

Fall 2014
SOME HELPFUL FORMULAE
1. Gamma function and properties:
(a)
() =
x1 ex dx
0
(b) For > 0, ( + 1) = ().
(c) For integers n 1, (n) = (n 1)!.
(d) (1/2) =
2. Binomial, parameter and n the number of trials
( )
n
p(k) =
(1 )nk k , k = 0, 1, 2, . . . , n .
k
3.
Western University (Ontario)  Also known as University of Western Ontario
STATS 3657

Fall 2014
SOME HELPFUL FORMULAE
1. Gamma function and properties:
(a)
() =
x1 ex dx
0
(b) For > 0, ( + 1) = ().
(c) For integers n 1, (n) = (n 1)!.
(d) (1/2) =
2. Binomial, parameter and n the number of trials
( )
n
p(k) =
(1 )nk k , k = 0, 1, 2, . . . , n .
k
3.
Western University (Ontario)  Also known as University of Western Ontario
STATS 2503

Winter 2015
Statistical Science 2503B Midterm Examination  February 11, 2015 2
1. (15 marks) Circle the correct answer.
d
(a) The solution to the differential equation 11% = tana: is
(A) y2+21nsinx=C y2+2lncosmzC
(C) y2—2sinx=C (D) y=v2coszc+C
(b) The solution to
Western University (Ontario)  Also known as University of Western Ontario
STATS 2122

Spring 2015
University of Western Ontario Department of Statistical and Actuarial Sciences
Statistics for Science STAT 222b
Instructor
Office
Section
Day
Time
Location
Sohail Khan Sohail Khan Email Office Hours
WSC276 WSC276
001 002
MW TTR
4:306:00 8:3010:00
B&GS 5
Western University (Ontario)  Also known as University of Western Ontario
STATS 2122

Spring 2015
Chapter 9 Solutions to Even Numbered Questions
9.14
Let denote the mean annual energy consumed per U.S. household.
(a) H0: = 92.2 million BTU (mean western household energy consumption is the same as all
American households)
Ha: 92.2 million BTU (mean wes
Western University (Ontario)  Also known as University of Western Ontario
STATS 2122

Spring 2015
Chapter 8 Solutions to Even Numbered Questions
8.16
(a) When x is normally distributed, the sampling distribution of sample mean is exactly normally
distributed. The confidence interval procedure 8.1 is based on this fact.
(b) When the sample size is larg
Western University (Ontario)  Also known as University of Western Ontario
STATS 2122

Spring 2015
5.
36
5.16
(a)
(b)
(c)
(d)
(e)
(f)
CHAPTER 5 ANSWERS
(a) P(T < 2.02) + P(2.02 g T g 2.02) + P(T > 2.02) = 1.
P(T < 2.02) = PtT > 2.02) = 0.05,
0.05 + P(2.02 g T g 2.02) + 0.05 = l, or
Since
(a)
Y
n 06400 0.1200 0.0400 0.8000
x 0.1200 0
Western University (Ontario)  Also known as University of Western Ontario
STATS 2122

Spring 2015
SS2122a  20080905
ASSIGNMENTS
Assignment #1: 1.7, 1.8, 1.11, 1.15, 1.30, 1.58, 1.62, 1.64, 1.66, 1.67
Answers to even numbered questions:
1.8: This study is descriptive. It is a summary of of the average salaries in professional
baseball, basketball an
Western University (Ontario)  Also known as University of Western Ontario
STATS 2122

Spring 2015
Assignment #3: 3.3, 3.4, 3.5, 3.7, 3.8, 3.10, 3.42, 3.48,
3.49, 3.52, 3.55, 3.73, 3.92, 3.93, 3.95, 3.102, 3.106,
3.121, 3.123, 3.124, 3.130, 3.131
Answers to Even numbered questions
Q 3.4: True.
Q 3.8: The median is more appropriate as a measure of centr
Western University (Ontario)  Also known as University of Western Ontario
STATS 2122

Spring 2015
1. A sample of the salaries of 100 female employees was taken from a large company
and the standard deviation of their salaries was found to be 20 (in thousands of dollars). If
the relationship between male and female salaries at the same company is x = 0