Econ 210 Spring Quarter 2009 Problem Set 3 - Due Date: 4/20/2009 Solve the following problem. Show your work 1. TRUE/FALSE a. Uncorrelated Random variables are also independent b. The correlation between two random variables will always be between 0 and 1
Econ 210 Spring Quarter 2009 Problem Set 5 - Solutions 1. True/False: a. The Central Limit Theorem ensures that an estimator is close to the true population value as the sample size gets large FALSE. That would be the LLN. b. An estimate is a random varia
Northwestern University
Department of Economics
STAT 210 Introduction to Statistics - Professor: Steffen Habermalz First Midterm Examination January 30th 2009 INSTRUCTIONS: Please read the whole exam first. Questions are not ordered by difficulty. Answer
Northwestern University
Department of Economics
STAT 210 Introduction to Statistics Professor: Steffen Habermalz First Midterm Examination February 1st 2008 INSTRUCTIONS: Please read the whole exam first. Questions are not ordered by difficulty. Answer al
Northwestern University
Department of Economics
STAT 210 Introduction to Statistics - Professor: Steffen Habermalz Second Midterm Examination May 11th 2007 INSTRUCTIONS: Please read the whole exam first. Questions are not ordered by difficulty. Answer all
Econ 210 Fruehling Quarter 2009 Problem Set 4 - Solutions 1. TRUE/FALSE a. The sample mean is a random variable TRUE. It varies from sample to sample and is constructed from random variables. b. One drawback of the sample median is that it is very sensibl
Practice Questions II Solutions 1. True/False (Dont forget an explanation) a) Chi-square random variables can be negative. FALSE. A Chi-square random variable is the sum of independent, squared standard normal variables and thus cannot be negative. b) The
Practice Questions II Normal Distribution Properties of the ND Calculating Probabilities Z-Transformation Standard Normal Distribution Cumulative Standard normal Critical values Summary of what we did: Chi-square distribution Random sample i.i.d. Sample S
Practice Questions IIa - Solutions 1. Assume you are sampling from a Normal Distribution with unknown mean and variance. a) You draw a sample of size 10 and calculate a sample mean of 33 and a sample variance of 225. Test the Null Hypothesis that the true
Practice Questions IIa 1. Assume you are sampling from a Normal Distribution with unknown mean and variance. a) You draw a sample of size 10 and calculate a sample mean of 33 and a sample variance of 225. Test the Null Hypothesis that the true mean of the
Northwestern University
Department of Economics STAT 210 Introduction to Statistics - Professor: Steffen Habermalz Second Midterm Examination February 22nd 2008 1. Write your name and circle your TAs name on the answer sheet. 2. (2+3=5 pts. each) True/Fal
Northwestern University
Department of Economics - STAT 210 Introduction to Statistics Professor: Steffen Habermalz - Second Midterm Examination February 20th 2009 INSTRUCTIONS: Read the whole exam first. Questions are not ordered by difficulty. Answer all
Econ 210 Spring Quarter 2009 Problem Set 3 - Solutions Solve the following problem. Show your work 1. TRUE/FALSE a. Uncorrelated Random variables are also independent FALSE. Uncorrelated RVs could share a non-linear relationship. b. The correlation betwee
Econ 210 Spring Quarter 2009 Problem Set 4 - Due Date: 5/6/2009 1. TRUE/FALSE a. The sample mean is a random variable b. One drawback of the sample median is that it is very sensible to the inclusion of outliers in the sample. c. Consider X~N(5,100). The
Econ 210 Fruehling Quarter 2009 Problem Set 5 Due Date: 5/11/2009
Solve the following Problems. Show your work. 1. True/False: a. The Central Limit Theorem ensures that an estimator is close to the true population value as the sample size gets large b. An
Econ 210 Spring Quarter 2009 - Problem Set 6 - Due Date: 5/27/2009 Solve the following Problems. Show your work. 1. True/False
a. You estimate a sample proportion p = 0.4 . The t-statistic corresponding to the null hypothesis that p=0.6 is t = 0.4 0.6
0.
Introductory Statistics Stats 210
Spring 2007
1
So what is this all about?
Lets assume we want to investigate the following relationships
What is the relationship between student performance and class size? What is the relationship between education and
Introductory Statistics Stats 210
Estimation & Hypothesis Testing
1
Estimation
Remember
We have described a population We have taken a sample from the population We have calculated the sample mean
Q: Why have we calculated the sample mean? A: To estima
Introductory Statistics Stats 210
Probability Distributions
1
The Normal Distribution
The Normal Probability Distribution, or Bell Curve, has only 2 parameters
Mean Variance
2 It is denoted by: X ~ N ( X , X )
Read: X is distributed normal with mean 2
Introductory Statistics Stats 210
Random Variables
1
What are Random Variables?
A random variable is a variable whose value is a NUMERICAL outcome of a random phenomenon
The sample space consists of elements that are not necessarily numerical The probab
Introductory Statistics Stats 210
Random Variables II
1
Relationships between TWO random variables
So far we were interested in ONE random variable Now we want to estimate the relationship between TWO random variables Example:
Relationship between wages
Regression Analysis
Introduction to Statistics STAT 210 Spring Quarter 2008
1
So what is this all about?
Lets assume we want to investigate the following relationships
What is the relationship between student performance and class size? What is the rela
Introductory Statistics Stats 210
Sampling, Sample Statistics and the Sampling Distribution
1
Sampling from a Population
Now that we described the population thoroughly we are ready to take a sample from the population Note: We assume that we take a rand
Econ 210 Spring Quarter 2009 Problem Set 1 - Solutions Solve the following Problems. Show your work. 1. A balanced coin is tossed three times. Denote H=heads, T=Tails, i.e. HHT stands for heads in the first 2 tries and tails in the third. a. What is the s
Econ 210 Spring Quarter 2009 Problem Set 2 - Solutions Solve the following problem. Show your work 1. TRUE/FALSE a. The median is a probability-weighted average of all possible realizations of a random variable FALSE. That is the definition of the mean (e
Practice Questions
1. True/False: State if the following statements are true or false. a. The sample space consists of all possible events. FALSE. Adding up all possible outcomes leads to double counting. b. If AB = then P(A|B)=0 TRUE. If AB = then P(AB =