(Probabilistic) Experiment: (, B, P )
is the sample space set of all possible outcomes. (Often denoted S.) denotes a particular outcome. = cfw_ all possible B is the class of "events" for which probabilities are defined. (We mainly ignore B in this clas
hOW TO GRAPH statistics
In statistics to graph a complete data set there is a few things to look at they are
the mean, median and if there is outliers. The mean and the median in data
determine the shape of the data graph. The median is the middle number
Notes 12
Recall:
The sample mean
x is the best estimate of the population mean .
This is an example of a point estimate.
Point Estimate: a single-value estimate of the population parameter.
Instead of being restricted to a single value for an estimate, a
Notes 11 addendum
DISTRIBUTIO OF THE SAMPLE MEA
Recall:
Since the sampling distribution of the sample mean, X ~
X = , X =
n
now follows a Normal distribution, we can use the standardizing formula
z=
x X
X
=
x
n
to find z-scores for sample mean calculation
Notes 11
Sampling distributions and the Central Limit Theorem
Recall:
Mean of a population:- denoted by the symbol (mu). This is a fixed parameter that is
unknown and is inferred from a sample.
Mean of a sample:- denoted by the symbol I (x-bar) is the ave
Notes 10
ORMAL APPROXIMATIO TO THE BI OMIAL
Recall: The parameters for the Binomial distribution are n and p.
Binomial probability calculations become tedious when n is large. For a large sample size n and
a suitable p, the Normal distribution can be used
Notes 9
ORMAL DISTRIBUTIO
Recall: The process of converting a Normal distribution X to the Standard Normal Z is called
standardization.
Standardizing a Normal Distribution:
USI G THE Z TABLE
The Z table is a listing of the probabilities associated with th
Notes 8
BI OMIAL DISTRIBUTIO
Bernoulli Trials
Bernoulli trials are trials that satisfy the following three conditions:
There are only two possible outcomes for each trial, called a success and failure
The probability of a success is the same for all trial
Notes 7
Random Variables
A random variable (r.v.) is a function whose values are 1) numerical and 2) depend on the
outcomes of a random process.
Simply put, a random variable is a quantity whose value depends on chance.
ote:
We usually use a capital lett
Notes 6
PROBABILITY and RA DOM VARIABLES
Random Process:
A process is said to be random if the outcomes of independent trials are
uncertain, but a pattern of outcomes emerges in the long run after very
many trials.
ote: Trials are independent if the outco
Chapter 3- Producing Data:
3.2 Designing Experiments:
Observation vs. Experiments:
An observational study observes individuals and measures variables of interest
but does not attempt to influence the responses. The purpose of an observational
study is to
Notes 4
BIVARIATE DATA
Bivariate data is data for which there are two variables for each observation.
Example:
The following bivariate data show the High school and college GPAs for 10 college sophmores.
High School 3.3 4.0 2.9 3.5 3.8 3.7 3.7 2.8 3.2 3.6
Chapter 3- Producing Data
Some questions to ask before producing data:
What is the group of interest?
What information about the group are we interested in?
How do we collect this information?
3.1 Design Samples:
Population, Sample:
The population in a st
(Continue) Chapter 1: Examining Distributions
1.2 Describing Distributions with numbers:
Center and Spread:
To get a useful numerical description of a distribution, we need to have both some
measure of center and some measure of spread.
Measuring center:
Chapter 1: Examining Distributions
Statistics is the science of data. We therefore begin our study of statistics by
mastering the art of examining data. Any set of data contains information about
some group of indiv
BoxPlots and Histograms
Boxplots and histograms are both charts that use quantitative data but they are very
different in the way the present them. Both of these graphs can have the same shapes but
the way they are presented. For boxplots when the mean is