3.7
1.
5
6
7
8
9
58
058
00235558
000035557
00022338
The distribution is skewed left and unimodal with a minimum of 55 and a
maximum of 98.
Percent
60
50
40
30
20
10
2.
0
StronglyAgree
a.
MildlyAgree
MildlyDisagree
StronglyDisagree
Percent
StronglyAgree
Mi
1
Chapter 4: Gathering Data
4.1: Experimental and Observational Studies
Does cell phone usage increase the chance
of cancer?
Study 1
A German study compared 118 patients with a rare
form of eye cancer to 475 healthy patients who did
not have the eye cance
4.3: Good and Poor Ways to Experiment
The elements of a good experiment
1. Control comparison group: the group which does
not receive a treatment (receives placebo
treatment) called control group.
2. Randomization: if you personally decide which
treatment
Sampling Distributions
1
Sampling distribution of Statistics
Transition Chapter to Inference
Questions:
1. Is parameter a constant or a random variable?
2. Is statistic a constant or a random variable?
The mean sample is a random variable. Its value is
STAT 3005: STATISTICAL METHODS
SPRING 2013
Hamdy Mahmoud
COURSE OUTLINE
Part I (ch1ch4): Gathering and exploring data.
Part II (ch5ch7): Probability, probability distributions,
and sampling distributions.
Part III (ch8ch10): inferential statistics
Part
2
Confidence interval for Mean,
Confidence Interval for population Mean,
Case 1: n is large or the population is normal
X
and
X ~ N ( , / n )
Z
~ N (0,1)
/ n
unknown
Replace with s and estimate the standard error in
the following way
s
SE X
n
n
A 95%
3
Determining the sample size, n
Determining Sample Size
Choosing Sample Size to have a certain level of
precision, a fixed MOE.
Very popular in polling applications like those seen
on MSNBC, Fox, CNN, etc.
A common question asked in practice.
FIRST: Samp
x
1
Sampling Distribution of x
We will find formulas for the mean and
standard deviation (standard error) of the
sampling distribution for mean.
We will see that the shape of the sampling
distribution for mean is approximately Normal.
We will notice th
Part III:
Inferential
Statistics
Chapter 10:
Comparing two groups
Hamdy Mahmoud
Stat. Dep.
Questions?
Do
you think , on average, females and males
are different in number of hours they study?
Construct a confidence interval for the difference.
Test if th
CASE 2:
COMPARING TWO GROUPS IN MEAN
(DEPENDENT SAMPLES)
Wilcoxon Signed Rank Test
1
Frank Wilcoxon (1882 1965)
WILCOXON SIGNED RANK TEST
The Wilcoxon signed rank test is a nonparametric
alternative to paired ttest.
Test
used when you have two dependen
Chapter 2: Exploring Data with graphs and
numerical summaries
2.1 Different Types of Data
2.1 Objectives
Know the definitions of
1.
a.
b.
c.
d.
2.
Variable
Categorical versus
quantitative variable
Discrete versus continuous
Frequency, proportion
(relative
Note: Dividing the totals by the sample size, will give
us the marginal probabilities
Grade
Male
Female
Totals
A
46
17
63/89=0.71
B
15
8
23/89=0.26
C
2
1
3/89=0.03
Total
63/89=0.71 26/89=0.29
89
Probability of C
Probability of Male
Note: Dividing the numb
Section 5.2

5.19
o The user can either click a link or enter the webpage or click out. The sample
space of the website is the five individual links.
 5.21
a) The probability is .248
b) .752
 5.22
a) .107*.107=.0114
b) The complement of this event is o
Section 3.3

3.86
o 95% of the students fall within the range of 470 to 674.
3.87
o 99.7% of the students fall within the range of 419 to 725.
3.94
a) Standard Deviation = 3
b) Standard Deviation = 1
c) The normal curve gets narrower as the standard devi
1.8
a) 40 Students
b) 3 Students
c) No because the students chose to stay after class, they were not selected
d) No because only 3 of the 40 students chose to stay after class which is not a large
enough sample. Furthermore, they were biased as they may h
6.7
For the SRS of 400, the P hat would be closer to the actual value of P than the P hat for the SRS
of 200 and sampling distribution would be closer to normal than the SRS of 200 because the
sample size is greater
6.8
a) Standard deviation = sqrt (.5*.5
STATISTICAL INFERENCE
Chapter 9: Tests About Hypothesis
Hamdy Mahmoud
VT, Stat. Dep.
Motivation Example: Magic Water
The Five Steps of a Significance Test
p
1. Assumptions
In chapter 7, under what conditions the sample proportion, p
, has Normal distribu
2.3 Measuring the center of quantitative data
Learning Objectives
1.
2.
3.
4.
5.
Calculating the mean
Calculating the median
Comparing the mean
& median
Definition of resistant
Know how to identify
the mode of a
distribution
Mean
The mean is the sum of th
STAT3005 students performance
in HW1HW6
Great
Class!
Comparing two groups in Mean
( 1 2 )
1.Confidence interval for (1 2 )
We have two cases:
1. CASE 1:
1 2
2
2
( x1 x2 ) t / 2, df
2
s
(i. e. max 4 )
2
smin
s12
s22
n1
n2
Degree of freedom can be calcu
1
Chapter 3: ASSOCIATION
Response and Explanatory variables
Response Variable/Dependent Variable (Y): outcome
variable on which comparisons are made
Explanatory Variable/Independent Variable (X):
Categorical : it defines the groups we compare with
respect
Descriptive Statistics: Homework 2 without extra points
Variable
N N* Mean SE Mean StDev Minimum
Q1
Median
Q3
Homework 2 80 11 46.675 0.685 6.127 15.000 46.000 48.500 49.875
Variable
Homework 2
Maximum
50.000
Great Class!
Probability in our Daily Life
Gam
Lecture 51
The Language of Probability
Thinking about Randomness
The Uses of Probability
RealLife Probabilities
Weather Forecasts
Sales Forecasts
Manufacture of Defective Product
ActuarialLife Tables
Internet Advertising
Simple Example
Suppose a Fa
Lecture 22
Populations and Samples
Types of Samples
Important Issues with Samples
Sampling People and Ethical Issues
Populations and Samples
Population: The entire group of individuals
about which we seek information.
Sample: The subset of the populati
Lecture 21
Ways to Collect Data
Designing Experiments
Basic Principles
Cautions
Obtaining Data
Available/historical data.
Observational study.
Design of Experiment.
Available Data
Relies on using historical data.
Surely, our historical data have the
Lecture 31
Graphical Displays of Data
Categorical versus Quantitative Variables
Displays for Categorical Variables
Displays for Quantittative Variables
Definitions
EDA: Exploratory Data Analysis is a set of
techniques used to explore and summarize
d
STAT3005 OnLine
Homework # 6
Summer I 2016
You must show all of your work for each problem in order to receive full credit. HW Due 06/24/2016.
*For Q1 and Q2 use the following problem*
Chocolate bars produced by a certain machine are labeled 8.0 oz. The
STAT 3005
Lecture 11: Introduction
Introduction
Introduction
1.1 Sources of Data
1.2 Describing Data
1.3 Probability and Statistical Inference
Three Stages of Statistical Analysis
1. Design How do we obtain the data?
2. Description How do we summariz
Stat 3005 OnLine
HW #2R
Summer I 2016
Homework Directions
Please read carefully the following directions
1. Open HW 2R homework in Scholar Test & Quizzes to answers the questions. Please also find
under resources some extra material to answer questions.
STAT 3005 On Line
Test 2
June 27, 2016
Take Home Test # 2 Directions
Please read carefully the following directions
1. You will submit your answers for this test on Scholar. You will have only one opportunity to submit the
test.
2. Complete this exam in y