A)
FIirst the variance of both samples are checked using the following hypothesis
1
2
1
2
H 0 : 2= 2
H1: 2 2
The p value of the test is greater than 0.05. So there is no sufficient evidence to reject the null
hypothesis. So it can be claimed that the vari
Examples for Lecture note
Example 1
If an IID random sample X 1 , X 2 ,., X n is taken from a population with mean , show that X is
unbiased for .
Example 2
Let X 1 , X 2 ,., X n denote a random sample from an exponential distribution with probability
fun
THEORY OF STATISTICS
Some important terms:
Statistics
Statistics is a science of data. This involves collecting, classifying, summarizing, organizing,
analyzing, and interpreting numerical information.
Descriptive statistics
Descriptive statistics utilize
THEORY OF STATISTICS
Interval estimation
Suppose is an estimator of . Then the error of estimation is defined as . When
estimating parameters we would like the error as small as possible. Since is a random variable
is also a random variable. Suppose we w
PERCENTAGE POINTS OF THE F DISTRIBUTION
The values in the table are those which a random variable with the F distribution on 1 and 2
degrees of freedom exceeds with probability 0.05 or 0.01.
Probability
2/1
0.05
1
2
3
4
5
6
7
8
9
10
11
12
14
16
18
20
25
3
Testing population means coming from two dependent populations
In some practical situations samples are considered to be dependent samples when the
subjects are paired or matched in some way.
Examples
1.Suppose a medical researcher wants to see whether a
DEPARTMENT OF STATISTICS AND COMPUTER SCIENCE
THEORY OF STATISTICS- ST 203
ACADAMEIC YEAR 2012/2013, SEMESTER II
TUTORIAL NO: 7-(Date of submission: November 27, 2013)
1. (a)
(b)
Define the significance level and power of the test 1- in statistical test o
DEPARTMENT OF STATISTICS AND CMOPUTER SCIENCE
THEORY OF STATISTICS- ST 203
ACADAMEIC YEAR 2012/2013, SEMESTER II
TUTORIAL NO: 4-(Date of submission: 16 September, 2013)
1.
Consider the random variable
with density given by,
(a) Find
, and the moment estim
PERCENTAGE POINTS OF THE 2 DISTRIBUTION
The values in the table are those which a random variable with the 2 distribution on degrees of
freedom exceeds with the probability shown.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
8/6/2013
Descriptive Statistics
Descriptive Statistics
Prof. P. Wijekoon
Department of Statistics & Computer
Science, Faculty of Science,
University of Peradeniya
What is Statistics?
Statistics is a science that deals with
data collection,
data organiza
STAT 5333
Inference One and Two Sample Questions
FALL 2016
1. A researcher reports that the average salary of assistant professors is more than $42,000. A
sample of 30 assistant professors has a mean salary of $43,260. The standard deviation of
the popula
Homeworks chapter 6
6.5
a)
According to the above results, the p value of the interaction effect is zero. So the interaction effect is
significant at 0.05 level. Therefore there is sufficient evidence to claim that the vibration rate is affected
by the in
Homeworks chapter 6
6.5a)
The p value of the two-way interaction is zero. So there is a significant interaction. The vibration affects
by both bit size and the cutting speed.
b)
Residual Plots for response
Versus Fits
99
4
90
2
Residual
Percent
Normal Pro
10/14/2016
Chapter 4 Randomized Blocks, Latin
Squares, and Related Designs
STAT 5333
1
4.1 The Randomized Complete
Block Design
Nuisance factor: a design factor that probably has
an effect on the response, but we are not interested
in that factor.
If th
10/27/2016
Chapter 5
Introduction to Factorial Designs
STAT 5333
Chapter 5
Design & Analysis of Experiments
8E 2012 Montgomery
1
Some Basic Definitions
Definition of a factor effect: The change in the mean response
when the factor is changed from low to h
Homework 7
13.1
According to the above results, the random interaction effect is not significant as the p value (0.927) is
higher than the significant level 0.05. When consider the main effects, there is no effect of operators as
the p value is high. But
DEPARTMENT OF STATISTICS AND CMOPUTER SCIENCE
THEORY OF STATISTICS- ST 203
ACADAMEIC YEAR 2012/2013, SEMESTER II
TUTORIAL NO: 3-(Date of submission: 9th September, 2013)
1. (a) Let
be a random sample taken from a uniform distribution with parameters
and
.