Stats 2035 Midterm #2 Practice Questions
1. Which statement is incorrect?
A) A Type I error occurs when we reject the null hypothesis when it should not be
rejected.
B) We failed to reject the null hypothesis, so it is proven that the null hypothesis is
t
Chapter 8 - Hypothesis Testing
Hypothesis Testing About when
is known - One Sided Tests
(section 8.3)
Confidence intervals are appropriate when
our goal is to estimate a population
parameter, in situations where you have no
idea what the value of or p or
Two Independent Samples
(sections 7.5, 7.6, 7.7)
We now take a look at two populations
Population 1 Population 2
random variable
x1
x2
mean
1
2
standard dev.
1
2
From each population, a random sample is
chosen
sample size
sample mean
sample std dev
Sample
Chapter 9 Comparing Two Populations
In chapter 8, we tested hypotheses about ,
the mean of a single population
We now extend these concepts to the case of
two populations
RECALL: sections 7.5, 7.6, 7.7
Population 1 Population 2
random variable
x1
x2
mean
One-sample Hypothesis Testing About the
Population Proportion, p
(section 8.6)
Recall from Section 6.2:
p
= population proportion of success
= proportion of the entire population
that has the specified attribute
p = sample proportion of success
= proporti
Independent Samples:
Inference For Two Population Means
when Population Standard Deviations are
Unknown (section 9.3/9.4)
There are two ways to calculate confidence
intervals and perform hypothesis tests about
1 2 when
1 and 2 are not known:
(I)
Pooled tw
Other Graphical Displays
1. Frequency Polygon
same horizontal axis as histogram
constructed by marking a point at the midpoint of
each class
height of graph is equal to the frequency of that
class
these points are then connected with straight lines
p
Chapter 2 Charts and Graphs
In this chapter we will learn about several
techniques for summarizing and depicting
data.
We will be interested in things like:
Constructing a frequency distribution from
a set of data
Describing/constructing different types
Chapter 3 Descriptive Statistics
In addition to graphing the data, we can gain
more insight by condensing the data into a
few single numbers which will summarize
the distribution in a clear and concise
manner
these single numbers are called statistics
t
What is Statistics?
Statistics is the science of collecting,
organizing, summarizing and interpreting
numerical facts, which we call data
Statistics start with a question
1. What percent of students at UWO
smoke?
2. Are there differences in the number of
Chapter 6 - Continuous Random Variables
A continuous random variable, x, can take
any value within a continuous region.
Probability Distribution
Recall: The probability distribution of a discrete
r.v. x is given as a table of all possible values of
x, alo
Measuring The Spread/Measures of
Variability (section 3.2)
Example
We are to compare four factories that are producing 600-ml
bottles of water. We need to determine which factory is
doing the best job. We take a sample of 5 bottles of water
from a selecte
The Normal Distribution (section 6.2)
In this section we discuss the most important
special type of continuous distribution:
The normal distribution
What Does a Normal Distribution Look
Like?
The density curve of a random variable that
follows the normal
Hypothesis Testing About when is
unknown (section 8.5)
As we saw in section 7.2, when the standard
deviation of the population, , is unknown,
we use the standard deviation of the sample,
s, in place of and we use the t-distribution
in place of the z-distr
Comparing Two Population: Paired
Differences (section 7.7)
Things start off as a 2-sample problem:
x1 = sample data from population1
x2 = sample data from population 2
In a paired differences situation,
subjects/people in an experiment (or sample)
are mat
Confidence Intervals for A Population
Proportion (section 7.4)
Studies often examine categorical data
categorical data consists of counts (x) or
percents (proportions, p) obtained from
counts
this section presents CIs for the unknown
proportion of succe
Business Statistics in Practice
Chapter 1: An Introduction to Business Statistics
Hristo Sendov
Department of Statistical & Actuarial Sciences
The University of Western Ontario
hssendov@stats.uwo.ca
Fall Semester 2013
Hristo Sendov
Business Statis
Outline
Business Statistics in Practice
Chapter 7: Condence Intervals
Hristo Sendov
Department of Statistical & Actuarial Sciences
The University of Western Ontario
hssendov@stats.uwo.ca
Fall Semester 2012
Hristo Sendov
Business Statis
Outline
7.1Z -Based condenc
Business Statistics in Practice
Chapter 10: Experimental Design and Analysis of
Variance
Hristo Sendov
Department of Statistical & Actuarial Sciences
The University of Western Ontario
hssendov@stats.uwo.ca
Winter 2014
Hristo Sendov
Business Statis
Outline
The Department of Statistical & Actuarial Sciences @UWO
Business Statistics in Practice
Chapter 9: Statistical Inference Based on Two
Samples
Hristo Sendov
Department of Statistical & Actuarial Sciences
The University of Western Ontario
hssendov@stats.uwo
Business Statistics in Practice
Chapter 14: Chi-Square Tests
Hristo Sendov
Department of Statistical & Actuarial Sciences
The University of Western Ontario
hssendov@stats.uwo.ca
Fall-Winter Semester 2012-2013
Hristo Sendov
Business Statis
Outline
14.1 Chi
The Department of Statistical & Actuarial Sciences @UWO
Business Statistics in Practice
Chapter 12: Multiple Regression and Model Building
Hristo Sendov
Department of Statistical & Actuarial Sciences
The University of Western Ontario
hssendov@stats.uwo.ca
Chapter 4:
Probability
Revision of Probabilities: Bayes Rule
An extension to the conditional law of probabilities
Enables revision of original probabilities with new information
Example 2
An article describes a cancer testing scenario
as below:
1% of
Chapter 1:
Introduction to
Statistics
Learning Objectives
LO1
LO2
LO3
LO4
Define statistics and list example applications of
statistics in business.
Define important statistical terms, including
population, sample, parameter, statistic, as they
relate to
Chapter 5:
Discrete
Distributions
The Poisson distribution is a discrete probability
distribution for the counts of events that occur randomly
in a given interval of time (or space).
X = The number of events in a given interval,
= mean number of events
Chapter 4:
Probability
Learning Objectives
LO1
LO2
LO3
L04
Describe what probability is and when one would use
it.
Differentiate among three methods of assigning
probabilities: the classical method, relative frequency
of occurrence, and subjective probabi
Chapter 8 - Hypothesis Testing
Type I and Type II Errors (section 8.2)
Suppose we are performing a hypothesis test
of
H0: = 0
Ha: 0
vs.
There are 2 possible errors that can be made:
Our
Decision
Do not
reject H0
Reject H0
True Situation
H0 is true
H0 is f
Measuring The Spread/Measures of
Variability (section 3.2)
Example
We are to compare four factories that are
producing 600-ml bottles of water. We need
to determine which factory is doing the best
job. We take a sample of 5 bottles of water
from a selecte