CHAPTER
Inferences for Two
Population Means
10
CHAPTER OBJECTIVES
CHAPTER OUTLINE
In Chapters 8 and 9, you learned how to obtain condence intervals and perform
hypothesis tests for one population mean. Frequently, however, inferential statistics
is used t
Binomial Distributions
This section focuses on a special type of a random variable
called the binomial.
In some statistical studies we perform an experiment
repeatedly. In this type of experiment, there are only two
outcomes. These two outcomes are either
Computing Formula for a Sample Standard Deviation
A sample standard deviation can be computed using the
computing formula s .
=
( ) (
(
1
)
2
)
Comparison of Measures of Dispersion?
Grouped-Data Formulas
When data are grouped in a frequency distribution,
Probability and the Life Sciences
When we are studying probability, we are
determining the likelihood of a certain situation
taking place.
Combining that with the Life Sciences, we could be looking
at the likelihood of two human parents with brown eyes
ha
Hm Enlnr and he Eula: Table 3.3.1 sham the mhtiumhip helm hair mint and
1:: mlur in: a Err-up at 1.170 Gennnn mm.
'I'IHI 1.2M Hltr CHIIH' Ind are cutw
tn Baum Em hlwk hair and wd hair" an: ninL if we chum inmemu:
at madam from thin Emup then Priblhct hair
Normal Curves
Normal distribution: is a distribution represented by a normal curve.
If a variable Y follows normal distribution, then it can be represented by
Y ~ N ,
.
N represents that the distribution is normally distributed,
represents the population
Effects of Transformations of Variables
There are a lot of reasons why it is more convenient to transform
a variable some of those reasons include:
1. You may want to change units from kg to
lbs
2. Your number may be very small such as
6.023.10-23 may b
Find the following probabilities: Pr(A), Pr(A or B), Pr(C and D),
Pr(D and E), Pr(D or E)
Probability Trees
Probability tree is a convenient way to break a problem down into
parts and organize information.
Example 7
A family has two children if the probab
GENG 200
Probability and Statistics
Review and Tutorial Exercises
Chapter 2
1
Brief Review
Sample Space
Event
Probability axioms
Addition Rule
Condition Probability
Multiplication Rule
Brief Review
Total Probability Rule
Bayes Theorem
Independenc
GENG 200
Probability and Statistics
Lecture Notes #4
Electrical Engineering Department
Qatar University
1
Chapter 2:
Probability
2
Chapter Outline
1.
Sample space and events
i.
ii.
iii.
iv.
2.
3.
4.
5.
6.
7.
8.
3
Random Experiments
Sample Spaces
Events
Co
Qatar University, College of Engineering
GENG 200
Assignment # 1 Solution
Due date: Oct. 12,2015
(1) (10 Marks) A car orders are summarized by the optional features that are requested as
follows:
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
GENG 200
Probability and Statistics
Lecture Note #6
Chapter 2:
Probability
1
Chapter Outline
1.
Sample space and events
i.
ii.
iii.
iv.
2.
3.
4.
5.
6.
7.
8.
2
Random Experiments
Sample Spaces
Events
Counting Techniques
Interpretations of probability
Addit
GENG 200
Probability and Statistics
Lecture Note #5
Chapter 2: Probability
Electrical Engineering Department
Qatar University
1
Chapter Outline
1.
Sample space and events
i.
ii.
iii.
iv.
2.
3.
4.
5.
6.
7.
8.
2
Random Experiments
Sample Spaces
Events
Count
Qatar University, College of Engineering
GENG 200
Assignment # 1
Due date:
(1) (30 Marks) Wires from a manufacturer are analyzed for conductivity and strength. The
results from 110 wires are as follows:
_ Strength _
High (HS)
Low (LS) High
Conductivity (H
The Use of Business Statistics in Management.
Managers have a huge responsibility to control and administer an organization or
parts of it. They face many complexities and they are always making decisions and taking
risks. The tool that helps managers mak
Chapter 3:
Discrete Random Variables and
Probability Distributions
3 Definitions
3-1 Probability Distributions, Discrete Random Variable
3-2 Probability Density Functions (PDF)
3-3 Cumulative Distribution Functions
3-4 Mean Value, Standard Deviation: Vari
Chapter 4:
Continuous Random Variables and
Probability Distributions
1
4-1 Continuous Random Variables
Continuous random variables- variables that can assume any
value in some range and infinite values within that range
Examples:
Measurement of current i
Introduction
The field of statistical inference consists of those
methods used to make decisions or to draw conclusions
about a population.
These methods utilize the information contained in a
sample from the population in drawing conclusions.
Statisti
6-1 Numerical Summaries
Definition: Sample Mean
6-1 Numerical Summaries
Example 6-1
6-1 Numerical Summaries
Fulcrum
The sample mean as a balance point for a system of weights.
6-1 Numerical Summaries
Population Mean
For a finite population with N measurem
Covered
Topics
8-1 Introduction
In the previous chapter we illustrated how a parameter can
be estimated from sample data. However, it is important
to understand how good is the estimate obtained.
Bounds that represent an interval of plausible values for