Binomial Experiment
A binomial experiment is an experiment which satisfies these four conditions
A fixed number of trials
Each trial is independent of the others
There are only two outcomes
The probability of each outcome remains constant from trial t
Sampling and Sampling Distributions
Random Sampling
A sample is a group of objects or readings taken from a population for counting or measurement. We shall distinguish between two kinds of populations nite populations and
innite populations.
The sample m
Problems of Estimation
A common problem in statistics is to obtain information about the mean, , of a population.
For example, we might want to know
the mean age of people in the civilian labor force,
the mean cost of a wedding,
the mean gas mileage of
The Normal Distribution
Continuous Distributions
A continuous random variable is a variable whose possible values form some interval of
numbers. Typically, a continuous variable involves a measurement of something, such as the
height of a person, the weig
Summarizing Data: Measures of Variation
One aspect of most sets of data is that the values are not all alike; indeed, the extent to which
they are unalike, or vary among themselves, is of basic importance in statistics. Consider the
following examples:
In
Summarizing Data: Measures of Location
When we are about to describe a set of data, it is a sound advice to say neither too little nor too
much. Thus, depending on the nature of the data and the purpose we have in mind, statistical
descriptions can be ver
Possibilities and Probabilities
Counting
The Basic Principle of Counting: Suppose that two experiments are to be performed.
Then if experiment 1 can result in any one of m possible outcomes and if, for each outcome
of experiment 1, there are n possible ou
Some Rules of Probability
Sample Spaces and Events
We consider an experiment whose outcome is not predictable with certainty. However, we
suppose that the set of all possible outcomes is known.
DEFINITION: The set of all possible outcomes of an experiment
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Final Exam
Elementary Statistics
December 19, 2013
PLEASE READ THE FOLLOWING INFORMATION.
This is a 110-minute exam. Calculators are allowed. Books, notes, formula sheets, and
other aids are not allowed.
You are required to show all your work
Name:
ID#:
Final Exam
Elementary Statistics
May 15, 2014
PLEASE READ THE FOLLOWING INFORMATION.
This is a 110-minute exam. Calculators are allowed. Books, notes, formula sheets, and
other aids are not allowed.
You are required to show all your work and
Name:
ID#:
Midterm Exam
Elementary Statistics
October 17, 2013
PLEASE READ THE FOLLOWING INFORMATION.
This is a 75-minute exam. Calculators are allowed. Books, notes, formula sheets, and other aids
are not allowed.
You are required to show all your work
Name:
ID#:
Final Exam
Elementary Statistics
December 19, 2013
PLEASE READ THE FOLLOWING INFORMATION.
This is a 110-minute exam. Calculators are allowed. Books, notes, formula sheets, and
other aids are not allowed.
You are required to show all your work
Name:
ID#:
Final Exam
Elementary Statistics
May 15, 2014
PLEASE READ THE FOLLOWING INFORMATION.
This is a 110-minute exam. Calculators are allowed. Books, notes, formula sheets, and
other aids are not allowed.
You are required to show all your work and
Tests of Hypotheses: Means
We often use inferential statistics to make decisions or judgments about the value of a parameter,
such as a population mean. For example, we might need to decide whether the mean weight,
, of all bags of pretzels packaged by a
Summarizing Data: Listing and Grouping
Listing Numerical Data
Listing and thus, organizing the data is usually the rst task in any kind of statistical analysis.
EXAMPLE: Consider the following data, representing the lengths (in centimeters) of 60 sea
trou
Expectations and Decisions
Mathematical Expectation
EXAMPLE: Suppose we roll a fair, 6-sided die 100 times (keeping track of the results), and at
the end, we add up all the results of each roll. What would be the likely value of this sum?
Solution: The sa
Sampling Distribution of the Sample Means
Instead of working with individual scores, statisticians often work with means. What
happens is that several samples are taken, the mean is computed for each sample, and
then the means are used rather than individ
Conditional Probability
Recall that the probability of an event occurring given that another event has already
occurred is called a conditional probability.
The probability that event B occurs, given that event A has already occurred is
P(B|A) = P(A and B
Possibilities and Probabilities
Counting
The Basic Principle of Counting: Suppose that two experiments are to be performed.
Then if experiment 1 can result in any one of m possible outcomes and if, for each outcome
of experiment 1, there are n possible ou
One area of concern in inferential statistics is the estimation of the population
parameter from the sample statistic. It is important to realize the order here. The
sample statistic is calculated from the sample and the population parameter is inferred
(
Summarizing Data: Listing and Grouping
Listing Numerical Data
Listing and thus, organizing the data is usually the rst task in any kind of statistical analysis.
EXAMPLE: Consider the following data, representing the lengths (in centimeters) of 60 sea
trou
Summarizing Data: Measures of Location
When we are about to describe a set of data, it is a sound advice to say neither too little nor too
much. Thus, depending on the nature of the data and the purpose we have in mind, statistical
descriptions can be ver
Multinomial Probabilities
A multinomial experiment is an extended binomial probability. The difference is that
in a multinomial experiment, there are more than two possible outcomes. However,
there are still a fixed number of independent trials, and the p
Standard Scores (z-scores)
The standard score is obtained by subtracting the mean and dividing the difference by
the standard deviation. The symbol is z, which is why it's also called a z-score.
The mean of the standard scores is zero and the standard dev
Probability Functions
A probability function is a function which assigns probabilities to the values of a
random variable.
All the probabilities must be between 0 and 1 inclusive
The sum of the probabilities of the outcomes must be 1.
If these two condi
Some Rules of Probability
Sample Spaces and Events
We consider an experiment whose outcome is not predictable with certainty. However, we
suppose that the set of all possible outcomes is known.
DEFINITION: The set of all possible outcomes of an experiment
Summarizing Data: Measures of Variation
One aspect of most sets of data is that the values are not all alike; indeed, the extent to which
they are unalike, or vary among themselves, is of basic importance in statistics. Consider the
following examples:
In
Probability Distributions
Random Variables
EXAMPLE: Consider rolling a fair die twice.
S = cfw_(i, j) : i, j cfw_1, . . . , 6
Suppose we are interested in computing the sum, i.e. we have placed a bet at a craps table.
Let X be the sum. Then X cfw_2, 3, .