26th Nov 2012
Measures of Relationship
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
23rd Nov 2012
Independent Samples HT
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.
21st Nov 2012
Comparing Two Groups
What if we want to compare two groups?
Males vs. Females
Control group vs. Medication group
How we compare these groups depends on
whether these groups are dependent or
What kind of study
19th Nov 2012
Types of Error
HTs for Proportions
p-value: Determined using the Normal
1500 randomly selected pine trees were
tested for traces of the Bark Beetle
infestation. It was found
16th Nov 2012
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
If the pvalue is p then
5% < p <= 10% t
12th Nov 2012
Hypothesis Tests (HT) : Chapter
A Hypothesis test is used to try and confirm
For Example: I want to know what average
height of the class is. So I draw a sample of
Based on the sample, I get t
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
We can now use our Tree Diagram to
21st Sept 2012
Between Variables (Section
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
28th Nov 2012
(Correlations Useless Cousin)
The Covariance is denoted by sxy.
Covariance is more useful from a
Because we use sxy to calculate r.
No Magnitude, Just Direction
30th Nov 2012
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
e.g. Smoking Causes Lung Cancer
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
19th Sept 2012
Boxplots and Shape
The box portion of the boxplot is very
useful in determining the shape of the
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
17th Sept 2012
Consider the data 1, 2, 3. Calculate the
Typical Percentages: The
For a nicely behaved distribution (i.e
fairly symmetric, no outliers), we expect to
About 68% of the observations
14th Sep 2012
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
3.Apply the median algorithm on the
19th Oct 2012
Coliform bacteria occur in river water with
an average intensity of 1 bacteria per 10
cubic centimeters (cc) of water.
(A)The probability there are no bacteria in a
20cc sample of water which is tested.
16th Oct 2012
An experiment where:
Two outcomes: Failure and Success
Multiple trials: repeat the experiment
more than once, i.e have n trials, where
S: the Pr(success) is the Same for each
15th Oct 2012
Let a be a constant and X a r.v. then:
E(a) = a
Var(a) = 0
Adding and Subtracting Random
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
12th Oct 2012
Sample Variance vs. Population
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?
In a game of chance the outcomes are -1
10th Oct 2012
The number of celery seeds that germinate
in a packet of 5 seeds has the following
What is the probability that le
1st Oct 2012
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
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?