1. The International Student Association at a certain university tracks all records of students from
abroad. The variables in the survey are (1)Name (2)Age (3)Country of Origin (4)Number of
countries visited before. 25 students were collected randomly amo
Stats 250 Lecture Notes
Introduction
Statistics.the most important science in the whole world:
for upon it depends the practical application of every other science and of every art:
the one science essential to all political and social administrat
Recitation 14: 4/18/2017
STT 200
1
Chapter 19: Confidence Intervals for Proportions
If we dont
p know the true proportion, p, we cannot calculate the standard deviation. Instead well use standard error,
SE(
p) = pq/n.
Oneproportion zinterval: p z SE(
p)
Recitation 11: 3/28/2017
STT 200
1
Chapter 16: Random Variables
A random variable is a numeric value based on the outcome of a random event. We denote this with a capital letter (ex:
X). We use a lowercase letter (ex: x) to denote a particular value. A di
Recitation 12: 4/4/2017
STT 200
1
Chapter 18: Sampling Distribution Models
1. a sampling distribution model for proportion is the distribution of all the different proportions from all possible
samples. We can model the sampling distribution as approximat
Recitation 15: 4/25/2017
STT 200
1
Chapter 20: Testing Hypotheses about Proportions
Null Hypothesis, H0 : proposes a value for a population parameter. H0 denotes no difference/effect/change/etc. Usually
in the form H0 : p = p0 where p0 is our hypothesized
Recitation 13: 4/11/2017
STT 200
1
Chapter 18: Sampling Distribution Models
1. A sampling distribution model for proportion is the distribution of all the different proportions from all possible
samples. We can model the sampling distribution as approxima
Probability Rules
Two additional rules for probability:
the general addition rule;
the general multiplication rule.
Conditional probability.
Independence.
Review: addition rule
Rule 3 (addition rule):
If two events have no outcomes in common, they a
r
Motivation
The preceding examples have one thing in
common: The number of sample points in each
of the sample spaces was small; hence, the
sample points were easy to identify and list.
How can we manage this when the sample
points run into the thousands
STT 315: Sampling Distribution
Huaxin Li
Huaxin Li ()
STT 315: Lecture 10
1 / 25
Content
1
2
3
The Concept of a Sampling Distribution.
The Sample Distribution of the Sample Mean and
the Central Limit Theorem.
The Sampling Distribution of the Sample
Propor
Understanding and Comparing
Distributions
Use boxplots to analyze the
distributions of quantitative
variables
Use timeplots to explore timerelated data
Boxplot
5number summary of a distribution
reports
min, Q1, median, Q3, max
Boxplots vividly displa
From Randomness to Probability
Definition of probability
Basic rules for probability
Use Venn diagram to represent ev
ents and their probabilities
Motivation
For a given coin, how can we know this coin is fair
? (A coin is fair if it has equal chance
Scatterplots, Association and
Correlation
The association of two quantitative variables
Use scatterplots to display the association o
f two quantitative variables (graphical metho
d)
Use correlation to measure the strength of t
he linear association of tw
Unit 1 Descriptive
Statistics
Data
Use tables to organize
data
Case & Variable
Categorical variable &
Quantitative variable
Case
subject
gender
age
high school GPA
college GPA
Case 1
1
m
32
2.2
3.5
Case 2
2
f
23
2.1
3.5
Case 3
3
f
27
3.3
3
Case 4
4
f
3
STT 315: Random Variable
Huaxin Li
Huaxin Li ()
STT 315: Lecture 9
1 / 46
Outline
1
Probability Distributions of Continuous Random
Variables
2
Normal Distribution
3
Probability Using TI 84 Plus: Normal
4
Percentiles Using TI 84 Plus: Normal
5
Standard Nor
Lab 9
Todays lab will explore the sampling distribution of the sample proportion p and construct normal theory
confidence intervals (CIs) for the population proportion p. This material is Sections 9.4 and 10.2 of the text.
[A  B] We should find in the ca
Review for the final exam
Chapter
5:
Law of large numbers
Central limit theorem
Normal approximation to binomial, Poission
Chapter 6:
Distributions derived from normal
Chapter 8: Estimation
MLE, MOM, CI, Fisher information , CR lower bound, asymptotic
CHAPTER 1_B
METHODS OF
GATHERING
DATA
1
KEY REMINDERS
POPULATION: THE ENTIRE GROUP OF
INDIVIDUALS OR INSTANCES ABOUT WHOM WE
HOPE TO LEARN.
POPULATION PARAMETER: NUMERICAL
CHARACTERISTIC OF A POPULATION (MEAN,
STANDARD DEVIATION, CORRELATION,
PROPORTION
Michigan State University
Department of Statistics and Probability
STT 456 Spring 12
TEST 1
Maximum 40, each question worth maximum 10
Name (Print):
Name (Sign):
1. For a whole life insurance issued to age (70), a death benefit of 1,000
is payable at the
PROJECT
Here is your first project. Use any software that you are comfortable with. You must
submit the relevant printouts. Please staple the sheets together and hand it over to your
TA during recitation on Thursday. DO NOT HAND IT DURING REGULAR CLASS
HO
STT200
Homework 3
Name _Kendra Lumpkin_
SECTION _006_ PID _A43013666_
Total: 10 points
Due two weeks from now.
Remember: neatness counts! 1 point if you dont staple your papers.
Chapter 11
On January 1 of every year, many people watch the Rose Parade on
STT200
Homework 4
Total: 10 points
Due two weeks from now.
Remember: neatness counts! 1 point if you dont staple your papers.
Chapter 17
1. An airline, believing that 5% of passengers fail to show up for flights, overbooks
(sells more tickets than there
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT 224
Correlation and Regression
Part 1
Chapters 12 and 13
Before beginning on next topic
Ttests and ANOVA
Used to test for differences in means among
groups that are classified by a nominal or
ordinal variable
Put another way, the Xvariable in ANO
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT224
Sampling Part II
Note: this material is not
covered in the book
What are we doing?
What do I want you to be able to do at the end
of this lecture?
1. Understand stratified random sampling
2. Follow a cookbook of formula when using
stratified rand
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT224
Sampling Part III
Systematic Sampling
My goals for this topic
Understand how systematic sampling is
useful
Have a basic understanding of the
computations associated with systematic
sampling
Understand limitations of systematic sampling
Systemat
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT224
Inference Part IV
Chapters 8 and 9
OneSample ttest
Third, compute tstatistic
Note use of absolute value
 x standard   x standard 
t
s
SE
n
The null hypothesis
This comes from the problem statement
Some one sample ttest examples:
Ho : st
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT224
Inference Part III
Interpretation
"Statistically significant" is not the same as "scientifically important". Before
interpreting the P value or confidence interval, you should think about the size
of the difference you are seeking. How large a diff
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT224
Correlation and Regression
Chapters 12 and 13
Correlation vs. Regression
Correlation
Simple Linear Regression
Used to:
1. If there is an association
between two variables
2. How strong it is
Does not assume cause and
effect
Neither variable is
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT224
Inference Part I
Chapter 8 in book
Inference
Statistical Inference is the process of
drawing conclusions (or making decisions)
about a population based on a sample
Weve already done this in the sampling part
of the course. When we estimate the me
Introduction to Probability and Statistics for Ecologists
STT 224

Spring 2017
STT224
Inference Part II
Bass Example
Our fisheries management objective for
largemouth bass in Park Lake is to have
an average length of 325 mm. We collect
a sample of 49 bass, and their mean
length is 267, with a sample standard
deviation of 37. Do we