Assignment 4
Brandon Solanki 40033595
20170312
1. Define the following terms in a sentence (or short paragraph) and state a formula if appropriate.
(a)Pvalue
Assuming Ho is true, it is the probabil
Assignment 3
Brandon Solanki 40033595
20170226
1. Define
1. Binomial Probability Distribution:
The model of probability obtaining one or two outcomes a certain number of times from a fixed
number of
ECONOMICS 2B03: Analysis of Economic Data I
Department of Economics
McMaster University
Assignment 1, Fall 2014, Due Tuesday September 16
Name and Student ID:
In order to facilitate grading, kindly co
ECONOMICS 2B03: Analysis of Economic Data I
Department of Economics
McMaster University
Assignment 2, Fall 2014, Due Tuesday September 30
Name and Student ID:
In order to facilitate grading, kindly co
ECONOMICS 2B03: Analysis of Economic Data I
Department of Economics
McMaster University
Assignment 3, Fall 2014, Due Tuesday October 21
Name and Student ID:
In order to facilitate grading, kindly comp
2B03 PART 5
Summary Statistics: Summation Notation
In statistics, we often need to accumulate or sum some variable of interest
Example: A might denote say income, with A1 being the income of the fir
2B03 Part 1
Variables and Distributions
In any statistical study, we analyze information/data obtained from
individuals
Individuals can be people, animals, households, plants, or any object of
inter
2B03 PART 9
Chapter 3
Origins of Data
Data can originate in a number of ways
Internal data is created as byproducts of regular activities
o Example: customer, employee, production data; government
2B03 PART 7
Shape Measures: Skewness
A frequency distributions degree of distortion from horizontal
symmetry
Pearsons (first) coefficient of Skewness is:
meanmode
o Skewness =
standard deviation
An
2B03 PART 6
The mode is the most frequently occurring value in the data set
o Can be found at either extreme of a data set
o May not appear in a data set at all because no single observation
occurs m
Introduction to R
I. Using R for Statistical Tables and Plotting Distributions
The R suite of programs provides a simple way for statistical tables of just about
any probability distribution of intere
Determining sample sizes for confidence intervals of given widths
Suppose that you are interested in knowing how large a sample size we need before, say , the
value of our estimated parameter lies wit
The sampling distrubution of the sample mean x
The sample mean X ~ = n ~1 nSUMi=1 Xi is an estimaaotr of the pipilation mean Omx
Expected value of X
The central limit theorem
The central limit theorem
Law of probability: Multiplication
Unconditional probability p(A)
o
The likelihood that a particular event will occur, regardless of where another event
occurs
Joint Probability p(A and B)
o
The likel
Basic rules for probability density functions
If a smooth curve is to represent a probability density functions, then the following tow
requirements must be met:
o
The total area between the curve and
Sampling Theory



Recall that sampling from a population is necessary for a umber of reasons
We now turn our attention to problems involving the estimation of means and proportions. We
shall be in
Background: Discrete Probability Distribution
A 'probability distribution' is the theoretical (i.e., analytical) counterpart of the frequency
distrbutions discussed earlier
By applying the laws of prb
Chapter 3
Origins of Data
Data can originated in a number of ways
Internal Data
Created as byproducts of regular activities
Example: customers, employee, productions records, governments records
Exte
Chapter 3. continuous
Basic probability concepts
We now lay the foundation for the field of statistical inference by studying the theory of
probability
Statistical inference
The set of techniques used
2B03 PART 8
Draw the median as a horizontal line in the box
Now extend the whiskers to the farthest points that are not suspected
outliers
Then for every point more than 1.5 times the IQR from the
2B03 PART 4
o Display data of 3 variables with height, width, and depth
Frequency histograms
o Horizontal axis
Identifies upper and lower limits of data classes
o Vertical axis
Shows number of obser
Cross Tabulations are tabular summaries for two variables
One variable represented by row heads
The other variable represented by column heads
Information for both variables entered in table cells
In
often we are interest in the proportion of successes in a smaple rather than the
number of success
recall that the sample proportion is denoted as P=x/n the random variable must
take on values 0,1 .n
ECONOMICS 2B03: Analysis of Economic Data I
Mo/We/Th 1:302:20 p.m., T13127
Department of Economics
McMaster University
Winter 2017
Contact information and office hours:
Professor . . . . . . . . .
Jan 11th
Summary statistics: symbolic expression
population parameter(typically unkown)
summary statistics based on population data
designated by greek letters
Sample statistics (computed from sampl
Handout for Example, Chapters 79
1
Mendels Pea Data
Mendels experiment resulted in n = 556 observations from which we calculate
Category
1 (RY)
2 (RG)
3 (WY)
4 (WG)
Null probability
Expected
Observed
CHEAT SHEET (I.E., STUDY AID) FOR 2B03
(8) For events A and B:
Pr[A B] = Pr[A] + Pr[B] Pr[A B]
= Pr[A] + Pr[B]
Below are some formulas that may help you when studying
for this course. This is in no wa
Handout for Regression, Chapter 10
Simple Regression Analysis
The (unknown) population regression line is given by
yi = 0 + 1 xi +
i
The sample regression line is given by
yi = b0 + b1 xi + i
A least
PROBABILITY TABLES (GENERATED BY R)
1. Standard Normal Cumulative Probability Tables.
Tables 1 and 2 provide values from the N (0, 1) (i.e. standard normal) distribution. Entries in cells are cumulati
continuous prob density functions
continuous random variables
unlike their discret counterparts, continuous random variables are uncotbale and
can assume any calue on the real number line
rather than
2B03 Part 3
o Ratio of a particular classs number of observations to the total
number of observations made
Relative frequency distribution
o Tabular summary of a data set
o Shows proportions of all o
2B03 PART 10
Errors in Survey Data
We expect that there will exist random error when we conduct a survey
Arises only in sample surveys (will be 0 in a census)
Equals the difference between:
o Value
2B03 Part 2
Chapters 1 & 2
Presenting Data: Tables and Graphs
When presenting data either in the form of tables or graphs, it is often
desirable to first split the data into groups/classes
How we sp
title: "2B03 Assignment 2"
author: 'Josh Powell: 400086238'
date: "Due Wednesday October 4 2017 (due in class prior to the start of the
lecture)"
output:
pdf_document: default
html_document: default
2B03 Assignment 1
Descriptive Statistics (Chapters 1 & 2)
Joshua Powell: 400086238
Due Wednesday September 20 2017 (due in class prior to the start of the lecture)
Instructions: You are to use R Markd