MATH& 146
Lesson 30
Section 4.3
Difference of Two Means
1
Difference of Two Means
For this lesson, we will consider a difference in two
population means, 1 2, under the condition that
the data are not paired.
For instance, a teacher might like to test the

Standard
Deviation
& Variance
OBJECTIVES
The learners are expected to:
a. Calculate the Standard
Deviation of a given set of
data.
b. Calculate the Variance of a
given set of data.
STANDARD DEVIATION
is a special form of average
deviation from the mean.

1
INTRODUCTION TO
STATISTICS & PROBABILITY
Chapter 5: Sampling Distributions
(Part 1)
Dr. Nahid Sultana
2
Chapter 5:
Sampling Distributions
5.1 The Sampling Distribution of a
Sample Mean
5.2 Sampling Distributions for Counts and
Proportions
3
5.1 The Samp

Objective
s
The student will be able to:
find the variance of a data
set.
find the standard deviation
of a data set.
SOL: A.9
2009
Varianc
e
Variance is the average
squared deviation from the
mean of a set of data. It is
used to find the standard
deviatio

Sampling and Sampling Distributions
Simple Random Sampling
Point Estimation
Introduction to Sampling Distributions
Sampling Distribution of
x
Properties of Point Estimators
n = 100
n = 30
1
Statistical Inference
The purpose of statistical inference is to

Statictics
Measure of Central Tendency
Skewness
Kurtosis
Mann Whitney u test
Measure of Central Tendency:
A measure of central tendency (also
referred to as measures of centre or
central location) is a summary
measure that attempts to describe a
whole set

Central Tendency:
A measure of central tendency (also referred to as measures of centre or central
location) is a summary measure that attempts to describe a whole set of data with a
single value that represents the middle or centre of its distribution.
T

Overview
Company
Profile
PHP
Working
of PHP
CMS
Features
Project
of CMS
Description
Technology
XAMPP
Snapshots
About Company
Recent Clients
PHP Introduction
PHPis aserver-side scriptinglanguage designed for
web development.
PHP is now installed

OUTLOOK
INTRODUCTION
USAGE
A SAMPLE CODE
OUTPUT
DATA TYPES
SPEED OPTIMIZATION
RESOURCES
INTRODUCTION
WHAT IS PHP?
PHPis a scripting langauge that was originally designed for web dovelopement to produce dynamic
webpages.
For this purpose,PHP code is embedd

Measures of central
tendency
Mean
Mode
Median
Mode
Distribution
of application for
admission to M.B.A. by discipline,
Findings,
The commerce category is the most
predominant.
Mode Grouped data.
Procedure,
1. Find the category or the class
interval which h

MATH& 146
Lesson 39
Sections 5.2 and 5.3
Regression Pitfalls
1
Don't Extrapolate!
Once you have verified the conditions and constructed
a linear model, then it can be used to approximate the
relationship between two variables.
However, these models have r

MATH& 146
Lesson 33.5
Inference Review
1
Instructions
Answer each of the following questions using
either a hypothesis test or confidence interval.
Where appropriate, be sure to give the
hypotheses, point estimate, standard error, test
statistic, and p-va

MATH& 146
Lesson 34
Section 4.4
ANOVA
1
ANOVA
To test whether observed differences in means could
have happened just by chance even if there was no
difference in the respective population means, we will
use the F statistic and ANOVA.
The method of analysi

MATH& 146
Lesson 32
Practical Significance
1
Example 1
Suppose a random sample of size 24 had a
sample mean of 33.8 and a sample standard
deviation of 9.8.
a) Test the hypotheses H0 : 30, H A : 30.
Use a significance level of 0.05.
b) Find the 95% confide

MATH& 146
Lesson 38
Sections 5.2
The Correlation Coefficient
1
Correlation
If the ordered pairs (x,y) tend to follow a straightline path, then we say that there is linear
correlation, or correlation for short.
2
Positive Correlation
A positive correlation

MATH& 146
Lesson 40
Sections 5.4
Inference for Linear Regression
1
Inference for Linear
Regression
Just as we identified standard errors for point
estimates previously, we can discuss standard
errors for the estimates of the slope and yintercept for a reg

MATH& 146
Lesson 33
Section 4.4
Comparing Many Means
1
Comparing Many Means
Sometimes we want to compare means across
many groups.
We might initially think to do pairwise comparisons;
for example, if there were three groups, we might
be tempted to compare

MATH& 146
Lesson 37
Section 5.2
Linear Regression
1
Linear Models
Fitting linear models by eye is open to criticism
since it is based on an individual preference. For
instance, it is not altogether clear whether lines A,
B, or C fit best in the scatterplo

MATH& 146
Lesson 27
Section 4.1
The t Distribution
1
Inference for Numerical Data
Earlier in this course, we introduced inference for
proportions using the normal model, and recently, we
encountered the chi-square distribution, which is
useful for working

MATH& 146
Lesson 28
Section 4.1
One-Sample Inference
1
T-Intervals from Start to Finish
1) Check the independence and normality conditions.
2) Use the sample mean, x, as the point estimate.
This is your "best guess" from your sample to
estimate the true (

Draft 1, April 1, 2016
JOHN F. KENNEDY SCHOOL OF GOVERNMENT
HARVARD UNIVERSITY
Entrepreneurial Finance II
MLD-839M
Fall Term 2 (aka, Mod 3)
(0.5 credits)
Carl Byers
Adjunct Lecturer in Public Policy
Harvard Kennedy School
[email protected]

1030-04 Quiz 1 Solution (Spring 2011)
(1.) [2 pts] The Venn diagram below tells us that
D
a.) C is a subset of D
b.) D is a subset of C
c.) C is disjoint from D.
C
(2.) [2 pts] Use braces to write the members of the following set: the days of the week.
cf

January 28
Name:
Problems 1 - 5: Choose the best answer to each of the following questions. Explain your
reasoning with one or more complete sentences.
1. (3 pts) If you multiply an area in square feet by a height in feet, the result will have
units of
c.

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THE NEW CITIZEN COMPANY
Savonetta
Point Lisas industrial
Estate
Date as postmark
Mr Michael Brinson
Saddle Road
Maraval
Dear Mr
You are cordially invited to attend a Sales Meeting on the last Friday of the next month at
2:30 pm in the small conference roo

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Electronic Document Preparation
Management
Mail Merge
Steps in creating a mail merge
Marvin Charles
Diane Sicobine
Shawn Joseph
9/28/16
Step One
Create the necessary document
First open Microsoft Word
then, type document's such as:
Letter , Email , Env