Graphs
Graphs are used to summarize and lassify data. There
are, just to name a few, pie harts, bar harts, and satter plots. Here are some examples:
Pie hart
1
Bar hart
2
Satterplot (x vs. y)
3
Another satterplot
4
Contour plot
We will speialize on one gr
Condence Intervals and Sample Size
Condence Intervals for the Mean (
known or n 30 and Sample Size)
Denition: A point estimate for a parame-
ter is the value of a statistic used to estimate
that parameter.
Example: Consider this sample taken from
a normal
The Binomial distribution
Let us consider ipping a coin n times. In such a random experiment, the ips of the coin are perceived to be
independent of each other. Since the coin has the same
probability of getting heads on any one of the ips, the
sum of the
Probability
Denitions
Sample Space
Denoted by the letter S , it is the set of all
possible outcomes from a random experiment
Event
Denoted by a capital letter from the beginning of the alphabet, an event is some subset
of a sample space
Examples
Let's rol
Condence Intervals and Sample Size
Condence Intervals for the Mean (
unknown and n < 30)
Fact: Suppose a random sample of size n
is taken from a normal population with mean
but a standard deviation that is unknown.
Then the random variable
t=
x
s
n
has w
Symmetry and Bias(Skewness)
For symmetric data, mean=median=mode
For right skewed data, mean>median>mode
For left skewed data, mean<median<mode
Symmetric
1
Right Skewed
2
Left Skewed
3
Condence Intervals and Sample Size for Proportions
How do you determine the true percentage of people
who prefer Coca-Cola to Pepsi?
How do the polls work?
What is the percentage points when you read a
poll?
How many people do you need to poll to get a ce
Questions and Answers pertaining to the
Central Limit Theorem
The central limit theorem: If you have a set of data
that came from some distribution, one you may not have
even heard of, with mean and standard deviation
and you have enough data (n 30), the
Discrete Probability Distributions
Random Variables
A random variable, i.e., r.v., is simply a variable which takes on values randomly from a
given sample space. R.V.'s are denoted by capital letters most usually from the end of the
alphabet.
Examples:
Le
Steps in Hypothesis Testing
In hypothesis testing, we start with a sample of data.
We then consider two hypotheses. These two hypotheses are populations from which we think that our sample
may have originated from.
Our problem is determining using some cr