STAT 1450 Recitation Activity 13
Inference about a Population Proportion
Name: _Victoria Hsu_
TA:
_Deborah K._
Date: _4/15/17_
OBJECTIVE
Students will compute confidence intervals for a proportion.
Students will use technology tools to verify results.
C
Normal Distribution
The Normal Distribution
Type of variable: Continuous (x)
Shape Symmetric (mound-shaped or bell-shaped)
Center Mean of x = median, because of symmetry
Spread i.e. variability, standard deviation measures
variability
Picture
68-95-99
Stat 1430
Recitation 7B
Probability Review
Bob thinks more female college students eat breakfast in the morning than males.
Suppose a survey of college students asked whether they ate breakfast this morning or not, along
with their gender. The results are
STAT 1430
Recitation 7A
Conditional Probability
Use the information below to answer #1-#7
28% of Fortune 500 companies are laying off employees. Moreover, 18% of those laying off employees are
cutting down on advertising expenses. Of those companies who a
TABLE A Table entry fat 2 is under the standard nunnal curve to the left Biz.
TABLE A Standard normal probabilities TABLE A Table entry for 2 is under the standard normal 01an In the left of 1.
TABLE A Standard normal probabilities (continued)
116
cfw_L7
STAT 1430
Recitation 12B (SOLUTIONS) Normal Approx/Sample Dist
Show all work. Use the table or normal approx. whenever they are appropriate. When using normal
approx., remember to check all conditions and remember your answer is only an approximation!
1.
STAT 1430
Recitation 12A (SOLUTIONS)
Binomial Distribution
Part 0:
A. What is the value of
( 42)
?
4321 24
= =6
( 42)= 2!42! ! = (21)(21)
4
B. What is the value of
(1615)
?
! 16
= =16
(1615)= 1516! 1! = 1615
15 ! (1) 1
C. If you wish to calculate the prob
Chapter 2 Tables and
Graphs for Summarizing
Data
Dr. Jonathan Baker
Stat 2450
Section 2.1 Types of Data
Univariate data is based upon a single characteristic, or, attribute.
Bivariate data is based upon two observations on each individual.
Multivariate da
Stat 2450
Autumn 2014
Recall from Chapter 3 that
The normal distribution is
very common
probably the most important distribution in statistics
Normal random variables can be modeled by unimodal, bellshaped curves.
Just like the parameters n and p speci
Chapter 1 An Introduction to Statistics
and Statistical Inference
STAT 2450
Section 1.1 Statistics Today
Statistics are used in numerous fields to describe
various phenomena.
USA Today (and other media) often include creative
graphical displays.
Section 1
Arts & Sciences
Department of Statistics
STATISTICS: 2450
INTRODUCTION TO STATISTICAL ANALYSIS I
SPRING 2017
Course overview
Instructor & Office Hours
Judit Bach
[email protected]
Office Information & Hours _
Teaching Assistant (to be completed by student)
STAT 2450 COURSE NOTES CHAPTER 2
TABLES AND GRAPHS FOR SUMMARIZING DATA
Section 2.1 Types of Data
_Univariate _data is based upon a single characteristic, or attribute, is a data
set.
_Bivarate_ data is based upon two observations on each individual.
Mult
STAT 2450 NOTES CHAPTER 3
NUMERICAL SUMMARY MEASURES
Section 3.1 Measures of Central Tendency
The tables and graphs from Chapter 2 provide useful ways to describe data.
Graphical techniques are a good start, but not appropriate for statistical inference.
STAT 2450 NOTES CHAPTER 1
AN INTRODUCTION TO STATISTICS AND
INFERENCE
STATISTICAL
Section 1.1 Statistics Today
Statistics are used in numerous field to describe various phenomena.
Youd be hard pressed to avoid data in your life. You can find data
anywhere
Chapter 4
Mathematical Expectation
4.1 & 4.2 Mean of a Random Variable
The value you expect to get in a statistical experiment is called the
Mean/Expectation/Expected Value of the random variable,
denoted by E[X ].
Example 1
Tossing a coin once
Let X deno
Geometric Distributions and Negative Binomial
Geometric Distribution
We repeat independent Bernoulli trials with success probability p.
Let X be the number of trials until the first success occurs. The
distribution of X is
P(X = x) = p(1 p)x1 ,
x = 1, 2,
Introduction to Mathematical Statistics
Lecture note 3
Instructor: Yuan Zhang
3.3 & 3.4 Continuous Probability Distributions
Example 1
Suppose we received a report of an accident on a freeway of 200
miles long. We are interested in how likely that it occu
Introduction to Mathematical Statistics
Lecture note 2
Instructor: Yuan Zhang
2.8 Total Probability Theorem and Bayes Theorem
Total probability theorem
We want to calculate P(A), but it is sometimes easier to find
P(A|B1 ), . . . , P(A|Bm ) and P(B1 ), .
Chapter 6
Some Continuous Probability Distributions
Name
Uniform
Beta
Notation
U[a, b]
Beta(, )
Normal
N (, 2 )
Exponential
Gamma
Chi-Squared
Exp()
(, )
2
= 2 , 2
P.D.F. f (x)
a x b.
x)1 , 0 < x < 1
1
ba ,
1
1
B(, ) x
(1
1
2
2
,
expcfw_ (x)
2 2
e x ,
<
4.8 Conditional Expectations
Definition: Conditional Expectation
If X is a discrete random variable, the conditional expectation of
u(X ) give Y = y is
X
E u(X )|Y = y =
u(x)P(X = x|Y = y )
x
Correspondingly, if X is a continuous random variable, the
con
Stat 4201, Spring 2017: HW 6 Solutions
In the 8th edition of the textbook do exercises: 5.16, 5.17, 5.23, 5.24, 5.40, 5.41, 5.51
In the 7th edition, these are: 5.16, 5.17, 5.23, 5.24, 5.40, 5.41, 5.51
5.16 If X Negative Binomial(k, ), then, in the books n
Stat 4201, Spring 2017: HW 5 Solutions
In the 8th edition of the textbook do exercises: 3.74, [with reference to 3.42 and 3.70, find Cov(X, Y )],
4.47, 4.49, 4.50, 4.58, 4.64, 4.80
In the 7th edition, these are: 3.74, 4.42, 4.46, 4.48, 4.49, 4.57, 4.62, 4
Stat 4201, Spring 2017: HW 4 Solutions
Problem 1. In the 8th edition of the book, do problems: 4.8, 4.10, 4.20, 4.33, 4.37, 4.38
In the 7th edition of the book, these are: 4.8, 4.10, 4.20, 4.34, 4.37, 4.38
4.8
Z
E(X)
3 1
=
1
Z
x2 dx +
x f (x)dx =
=
Z
0
3
STAT 4201, Spring 2017: Homework 7
This homework is due on Wednesday March 8 and will be graded by Guowei Li. Submit this
homework to the TA at the recitation you registered. Do not submit the homework
to the professor. You are encouraged to discuss with
Data Collection: Samples and
Surveys
Methods of Collecting Data
Observational Studies (part 1)
Most common observational study: Surveys
Experiments (part 2)
The difference between the two:
Observational- no influence, just record data
Experiment- ma
1) d
2) because The % of major varies according to gender. Female gender tends to have a higher
percentage in admin than male while male has a higher percentage in both finance and
accounting.
3) Female gender tends to have a higher percentage in admin th
Data Collection: Samples and
Surveys
Methods of Collecting Data
Observational Studies (part 1)
Most common observational study: Surveys
Experiments (part 2)
The difference between the two:
Observational: no influence, just record
Experiments: manipula
Data Collection: Experiments
Designing Experiments
What is an experiment?
What makes a good experiment?
Different designs of experiments
Observational studies
An observational study
Observes individuals
Without influence
Measures variables and makes