STAT 101 - Agresti
Homework 3 Solutions
9/27/10
Chapter 4
4.27. (a) The sampling distribution of the sample proportion of heads for flipping a balanced coin once is
p
0
1
Probabilit 0.5
0.50
y
0
(b) The sampling distribution of the sample proportion of he
11. Multiple Regression
y response variable
x1, x2 , , xk - a set of explanatory variables
In this chapter, all variables assumed to be quantitative.
Multiple regression equation (population):
E(y) = + 1x1 + 2x2 + . + kxk
Parameter Interpretation
= E(y)
10. Introduction to Multivariate
Relationships
Bivariate analyses are informative, but we usually need
to take into account many variables.
Many explanatory variables have an influence on any
particular response variable.
The effect of an explanatory va
9. Linear Regression and Correlation
Data: y: a quantitative response variable
x: a quantitative explanatory variable
(Chap. 8: Recall that both variables were categorical)
For example (Wagner et al., Amer. J. Community Health, vol. 16, p. 189)
y = mental
8. Association between
Categorical Variables
Suppose both response and explanatory variables are
categorical. (For comparing means in Chap. 7,
response variable is quantitative, explanatory variable
is categorical. Chap. 9 considers both quantitative.)
7. Comparing Two Groups
Goal: Use CI and/or significance test to compare
means (quantitative variable)
proportions (categorical variable)
Group 1
Population mean
Population proportion
1
1
Group 2
2
2
Estimate
y2 y1
2 1
We conduct inference about the diff
6. Statistical Inference:
Significance Tests
Goal: Use statistical methods to test hypotheses such
as
Mental health tends to be better at higher levels of
socioeconomic status (SES) (i.e., there is an effect)
For treating anorexia, cognitive behavioral an
5. Statistical Inference: Estimation
Goal: Use sample data to estimate values of
population parameters
Point estimate: A single statistic value that is the
best guess for the parameter value
Interval estimate: An interval of numbers around the
point estim
4. Probability Distributions
Probability: With random sampling or a
randomized experiment, the probability an
observation takes a particular value is the
proportion of times that outcome would occur in
a long sequence of observations.
Usually corresponds
12. Comparing Groups: Analysis of
Variance (ANOVA) Methods
Response y
Categorical
Explanatory x vars
Method
Categorical
Contingency tables
Quantitative
Quantitative
Regression and correlation
Quantitative
Categorical
ANOVA
(Where does Ch. 7 on comparing 2
What Is Culture?
T he Conceptual Question
wag.» ;. "
The anthropologist sees culture as the shared ideas and behavrors of a group of people.
These Trobriand island women are assembling yams they have harvested in preparation for a
feast.
I
l
i i
Formula Card Exam 2 STA3123
Steps for constructing the Condence Interval for the True Difference between the Population Means
(large, independent samples]:
2
o 02
Step 1 Gather Data from Problem, Calculate X1 X2 , and Calculate 1+ 2 .
1 "2
Step 2 Find 2m
7.5 - Confidence Intervals for Means
psu.edu
Previously we considered confidence intervals for 1-proportion and
our multiplier in our interval used a z-value. But what if our variable
of interest is a quantitative variable (e.g. GPA, Age, Height) and we
w
8.2 - Hypothesis Testing for a
Proportion
psu.edu
Here we will be using hypothesis tests to compare a proportion in one
group to a specified population proportion.
Examples: Research Questions
The following are research questions that could be answered
us
8.4 - Hypothesis Testing for a Mean
psu.edu
Hypothesis testing for one mean will use the same five steps with a
few small changes. This is procedure is known as a one sample mean
t test.
Five Step Hypothesis Testing Procedure
1. Check any necessary assump
7.2 - Confidence Intervals for
Proportions
psu.edu
Lets begin by constructing a confidence interval for a population proportion. For the following procedures, the assumption is that both
np 10np10 and n(1 p) 10n(1p)10. If pp is unknown, use pp^ as
an esti
3. Descriptive Statistics
Describing data with tables and graphs
(quantitative or categorical variables)
Numerical descriptions of center,
variability, position (quantitative variables)
Bivariate descriptions
1. Tables and Graphs
Frequency distribution
2. Sampling and Measurement
Variable a characteristic that can vary in
value among subjects in a sample or a
population.
Types of variables
Categorical (also called qualitative)
Quantitative
Categorical variable scale for
measurement is a set of catego
STAT 101 - Agresti
Homework 2 Solutions
9/17/10
Chapter 3
3.33. The mean, standard deviation, maximum, and range all increase, because the observation for D.C.
was a high outlier. Note that these statistics are not resistant to outliers. On the other hand
STAT 101 - Agresti
Homework 1 Solutions (including optional exercises)
9/2/10
1.2. (a) Population was all 7 million voters, and sample was 2705 voters in exit poll. (b) A statistic is the
56.5% who voted for Schwarzenegger from the exit poll sample of siz
Statistics 101: Formulas Final Exam
y=
yi
n
s2 =
y
se = s/ n
y =
n
z=
y t(se)
t=
y 0
se
z=
0
=
0 (1 0 )
n
z (se) se =
n = (1 )
n = 2
z
M
(2 1 ) z (se), se =
t = (y 2 y 1 )/se,
2 =
(y y )2
n1
z
M
(1 )/n
2
2
1 (1 1 ) 2 (1 2 )
+
n1
n2
(y 2 y 1 ) t(se)
11. Multiple Regression
y response variable
x1, x2 , , xk - a set of explanatory variables
In this chapter, all variables are assumed to be
quantitative. Chapters 12-14 show how to incorporate
categorical variables also in a regression model.
Multiple re
10. Introduction to Multivariate Relationships
Bivariate analyses are informative, but we usually
need to take into account many variables.
Many explanatory variables have an influence on any
particular response variable.
The effect of an explanatory v
4. Probability Distributions
Probability: With random sampling or a
randomized experiment, the probability an
observation takes a particular value is the
proportion of times that outcome would occur in
a long sequence of observations.
Usually corresponds