College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
Introduction to Confidence
Intervals
Confidence Intervals for a
Proportion
Problem:
You play a game and win 136 out of 270 times.
Estimate the probability of winning the game.
Proportions
0 p 1
The parameter p represents the proportion of the
p
population
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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WOMEN STUD 200

Fall 2016
Statistics
Review test 4
SI: Lori
Hypothesis testing for means
Dependent (paired)
Mean
(2 samples)
Both samples are large
(n>30)
Independent
ANOVA
Mean
(3 samples)
Scheffe Test
At least one
sample is
small
Pooledvariance
Fail to test
reject
Test
variance
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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WOMEN STUD 200

Fall 2016
Introduction to
Hypothesis Testing
Hypothesis testing is a decisionmaking
process by which we analyze a sample in an
attempt to distinguish between results that
can easily occur and results that are unlikely.
The process begins with a claim or statement
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Review for Quiz 2
Lori
Summary
Confidence Interval
Hypothesis Testing
Sample #
One sample
Two samples
Three ways
Critical value
Pvalue
Confidence Interval
Five steps
Step 1
Identify the null hypothesis (and the clai
m).
Hypothesis: a claim or state
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 9: Means
Two sample hypothesis testing: compare 2 different
populations.
means
independent samples
dependent samples (paired data)
variances
Means: dependent samples.
Assumptions:
d 0
Dependent samples
(paired
d 0,
d data).
0, d 0
Find the d
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 10
In 1964, Eric Bram, a typical New York City teenager,
noticed that the cost of a slice of cheese pizza was
the same as the cost of a subway ride. Over the
years, he noticed that those two costs seemed to
increase by about the same amounts. In 1
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 4
Sections 2,3,4,5,8
Definitions:
A probability experiment is a
chance process that leads to
welldefined results called
outcomes.
A simple event is the outcome
of a single trial of a probability
experiment.
The sample space is the set of
all poss
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 9
Proportions
Two sample hypothesis testing: compare 2 different
populations.
5
np
nq 5
p1 p2
x1 x2
Proportions.
1 p
2)
(p
(
p
p
)
1 2 p
z
Assumptions: For each sample,
and n1 n2
1 1
pq
q 1 p
n
n
1
2
Null hypothesis:
Test value:
p
2 ) E
(p
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 3
Recall
Definition:
A statistic is a characteristic or measure obtained by using the
data values from a sample.
A parameter is obtained by using all the data values of the
population.
Measures of center:
Mean
Median
Mode
Midrange
x
Mean:
x
n
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
Chapter 8
Hypothesis Testing:
Proportions
np 5, nq 5
p
p
Test for a proportion:
z
pq/ n
Test value:
H1 : p 12
Note: for questions about a (significant) majority we
have
The Gallup Poll reported that 45% of individuals felt they
were worse off than 1 y
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Mathematics 117Q  Introduction to Probability and Statistics
Fall 2015
Dr. Robert Bailey, Dr. Karen Rogers
Text and materials: Elementary Statistics, 12th or 11th ed., Mario F. Triola;
Calculator (TI83, TI83 PLUS, TI84 or TI84 PLUS recommended)
Cours
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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WOMEN STUD 200

Fall 2016
Review for Chp1, 2 and 3
Lori
Chapter 1
The vocabulary from the textbook
Levels of measurement
nominal ordinal interval ratio
Types of sampling
simple random, random, systematic, stratified, cluster, convenience
Examples from history when samples were
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
Chapter 7
Means
Given a sample with mean 5 and standard deviation 2,
estimate .
x
The best point estimate of
is .
x / n
x
distribution of the mean has
Recall that the sampling
and
.
[x E, x E]
E z /2 x z /2 / n
Confidence Interval:
1
where
and the
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
Chapters 1 and 2
Chapter 1:
Learn the vocabulary from the textbook.
(All boldfaced words.)
Statistics is the science of planning and conducting
studies to
collect,
organize,
summarize,
analyze, and
draw conclusions from data.
Descriptive statistics
Data a
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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WOMEN STUD 200

Fall 2016
Chapter 13 (nonparametric tests)
Advantages and disadvantages of nonparametric tests:
(p. 636)
Disadvantages: less sensitive, less efficient
Advantages: Distributionfree, hypotheses not involving
parameters, use for nominal or ordinal data.
Wilcoxon ra
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 4
Sections 2,3,4,5,8
Definitions:
A probability experiment is a
chance process that leads to
welldefined results called
outcomes.
A simple event is the outcome
of a single trial of a probability
experiment.
The sample space is the set of
all poss
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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WOMEN STUD 200

Fall 2016
Chapter 6
( x ) 2 /2 2
e
y
2
The Normal Distribution
A family of curves with parameters and
.
Properties:
Symmetric, bellshaped, mean=median=mode.
Continuous probability distribution: y>0, area under the
curve=1.
Probabilities determined by area: P
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 9
Proportions
Two sample hypothesis testing: compare 2 different
populations.
5
np
nq 5
p1 p2
x1 x2
Proportions.
1 p
2)
(p
(
p
p
)
1 2 p
z
Assumptions: For each sample,
and n1 n2
1 1
pq
q 1 p
n
n
1
2
Null hypothesis:
Test value:
p
2 ) E
(p
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Chapter 5
A random variable, X, is a variable whose values are
determined by chance.
discrete  examples: number showing on a die
number of students in class
continuous  example: height in inches
Discrete probability distribution (pdf)
P(X) is a function
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
THE
PALACE
THIEF
ETHAN CAN IN
Picador USA
New York
TIIF. rAt.AC~ TH1H~, Copyrighl CI 1994 by F.lh~n C~nin. All rlghl$
Il:KT\l:d. rrinted in the United Statn of Amcric~. No part of Ihis
book may be used or reproduced in any manm:r whal5OC'l:r
.l1houl " 'nl
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
H 0 : 1 12
2 (ANOVA)
3
Chapter
Oneway ANOVA
1 2 (Analysis of Variance)
Test for equality of means for 3 or more samples.
1 3
2 3
Do pairwise testing only if a significant difference is
found.
Assumptions:
interval or ratio data
independent samples
no
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
Confidence Intervals
Lori
Overview
Proportion
Confidence Intervals
Confidence Level
How to find the Sample Size
Proportions
0 p 1
The parameter p represents the proportion of the
p
population with a certain characteristic
(success).
x number of succe
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
Chapter 11
2
distribution (p.362)
This is the distribution of sample variances (when
samples of size n are taken from a normally distributed
population).
It is a family of curves based on degrees of freedom.
For samples of size n, there are n1 degrees of
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
women study
WOMEN STUD 200

Fall 2016
Overview
Hypothesis testing for proportions
One sampletwo outcomes (success/failure)
Two samplestwo outcomes each sample
2
Distribution
Goodnessoffit test
Test for Independence
Test for Homogeneity of proportion
Hypothesis testing for means
One s
College of Nursing, The Children's Hospital & Institute of Child Health, Lahore
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Fall 2016
Vocabs Review
Parsons
Sample space: The set of all possible outcomes of an experiment
Population is the complete collection of all elements (scores, peo
ple, measurements, and so on) to be studied.
A census is the collection of data from every member o