Lecture 32
26th Nov 2012
Ans:
Conclusion:
Measures of Relationship
Chapter 12
We want to know the relationship between
two random variables, X and Y.
To start, we can plot them using a
scatterplot (i.e a plot of all X and Y
coordinates) e.g
Three Measur
Lecture 31
23rd Nov 2012
Independent Samples HT
CAREFUL!
How you define your Ha affects:
1. P value
2. The calculation of d
IF you change the direction of your Ha then
everything else must change as well.
Your final answer WILL NOT change.
Example
A resea
Lecture 30
21st Nov 2012
Comparing Two Groups
What if we want to compare two groups?
Example:
Males vs. Females
Control group vs. Medication group
How we compare these groups depends on
whether these groups are dependent or
independent.
What kind of study
Lecture 29
19th Nov 2012
Ans:
Types of Error
HTs for Proportions
Hypothesis:
Formula:
p-value: Determined using the Normal
table.
Conclusion
Example:
1500 randomly selected pine trees were
tested for traces of the Bark Beetle
infestation. It was found
Lecture 28
16th Nov 2012
Recall:
Significance Level 2 Views
1.Black and White
- The question gives you a significance
level, i.e. 5%. If pvalue < significance level
then reject Ho.
Significance Level 2 Views
2.Grey
If the pvalue is p then
5% < p <= 10% t
Lecture 27
12th Nov 2012
Hypothesis Tests (HT) : Chapter
7
The Concept
A Hypothesis test is used to try and confirm
a suspicion.
For Example: I want to know what average
height of the class is. So I draw a sample of
students.
Based on the sample, I get t
Lecture 11
3rd Oct 2012
Sampling Without Replacement
An experiment is done where two cans
were selected from a container
consisting of 15 pop and 17 juice.
Selections were done WITHOUT
replacement.
Tree Diagram:
We can now use our Tree Diagram to
solve
Lecture 6
21st Sept 2012
Examining Relationships
Between Variables (Section
2.5)
Problem: Does the stress of machinery
affect the ability of a soya plant to grow?
Further, does the amount of light influence
its ability to grow?
Plan: 52 seeds were potte
Lecture 33
28th Nov 2012
Recall:
Covariance
(Correlations Useless Cousin)
Notation:
The Covariance is denoted by sxy.
Purpose:
Covariance is more useful from a
statisticians perspective.
Because we use sxy to calculate r.
No Magnitude, Just Direction
Wit
Lecture 34
30th Nov 2012
Causation
Often we want to use data collected from
an experiment to asses whether or not
there is evidence that X affects Y, i.e. Do
changes in X cause a change in Y. This is
called Causation.
e.g. Smoking Causes Lung Cancer
e.g.
Question I:
The probability that the gestation period of a woman will exceed 9 months is 0314.
a) Let X be the number of human births in which the gestation period exceeds 9 months
among, 6 births. Specify the distribution of X and give the conditions th
Lecture 5
19th Sept 2012
Boxplots and Shape
The box portion of the boxplot is very
useful in determining the shape of the
distribution.
Symmetric: The median lies in the
centre of the box
Skewed to the right: The median is
closer to Q1 than it is to Q3
Sk
Lecture 4
17th Sept 2012
Example:
Consider the data 1, 2, 3. Calculate the
standard deviation.
Typical Percentages: The
Empirical Rule
For a nicely behaved distribution (i.e
fairly symmetric, no outliers), we expect to
find:
About 68% of the observations
Lecture 3
14th Sep 2012
Algorithm: Q3
1.Start by finding the median using the
algorithm discussed before.
2.Look at all observations to the right of
the median (Not including the median
value).
3.Apply the median algorithm on the
remaining data.
4.This v
Lecture 17
19th Oct 2012
Example:
Coliform bacteria occur in river water with
an average intensity of 1 bacteria per 10
cubic centimeters (cc) of water.
Find:
(A)The probability there are no bacteria in a
20cc sample of water which is tested.
(B)The pr
Lecture 16
16th Oct 2012
Physical setup:
An experiment where:
Two outcomes: Failure and Success
Independent trials
Multiple trials: repeat the experiment
more than once, i.e have n trials, where
n>1
S: the Pr(success) is the Same for each
trial
Pr(Succes
Lecture 15
15th Oct 2012
Constants
Let a be a constant and X a r.v. then:
E(a) = a
Proof:
Var(a) = 0
Proof:
Adding and Subtracting Random
Variables
Let a be a constant and X, Y be r.v.s then:
1.E(X + Y) = E(X) + E(Y)
2.E(X Y) = E(X) E(Y)
If X and Y are IN
Lecture 14
12th Oct 2012
Sample Variance vs. Population
Variance
Experiment: Roll a fair die 3 times and
observe a 2,5,6.
What is the sample Variance?
What is the population Variance?
Why the difference?
Example:
In a game of chance the outcomes are -1
Lecture 13
10th Oct 2012
Recall:
F(x)
1
2
3
F(x)
1
2
3
F(x)
1
2
3
Example
The number of celery seeds that germinate
in a packet of 5 seeds has the following
cdf:
X
0
1
2
3
4
5
F(x)
0.1
0.2
0.3
0.5
0.8
1
Questions follow.
What is the probability that le
Lecture 10
1st Oct 2012
Question:
It is known that 70% of the time you bike to
class, and 30% of the time you take the
bus. If you take the bus to class in the
morning there is a 20% chance youll
arrive late. When you go by bicycle there
is a 10% chance
Lecture 9
28th Sept 2012
Conditional Probability and Tree Diagrams
What are Tree diagrams?
Visual display of branches and nodes, where at
each node a choice is made.
When do we use them?
In conditional probability problems.
How do we use them?
Each branch