Ch. 7,8,9
Name:
04/12/2015
Exam #3 Math 227
Show all work for full credit.
1.). In a survey of 1000 people, 700 said that they voted in a recent presidential election. Voting records show
that 61% of eligible voters actually did vote.
a. Construct a 96% c
Type I & Type II
Errors
Type I and Type II Errors:
When testing a null hypothesis, we arrive at a conclusion of rejecting it
or failing to reject it. Such conclusions are sometimes correct and
sometimes wrong even if we do everything correctly. Errors exi
Chapter 9
Lecture 2
Section: 9.5
This section presents a method for using two samples to compare the
variances of the two populations from which the samples are
drawn. We know that variation in a sample can be measured by the
standard deviation or varianc
Chapter 9
Inferences from Two Samples
Lecture 1
Sections: 9.1 9.2
There are many real and important situations in which it is necessary
to use sample data to compare two population proportions. We
may want to compare the percentage of males and females in
Chapter 7
Lecture 2
Section: 7.2
Percentage-Probability-Proportion
Although this section focuses on the population proportion p, the
procedures discussed here can also be applied to probabilities or
percentages, but percentages must be converted to propor
Chapter 7
Estimates and Sample Sizes
Lecture 1
7.3 7.4
Confidence Intervals
We will now work with inferential statistics. Recall that inferential
statistics are methods used to draw inferences about a population
from a sample. Thus, we will use sample dat
4/10/15
Chapter 6
Normal Approximation to
Binomial
Lecture 4
Section: 6.6
Normal Approximation to
Binomial
Recall from Chapter 5, the Binomial Probability Distributions:
1. The procedure must have a fixed number of trials.
2. The trials must be independen
4/10/15
Chapter 6
Normal Probability Distribution
Lecture 1
Sections: 6.1 6.2
Probability Density
Recall form Chapter 5,
Random Variable: A variable having a single numeric value that is
determined by chance, for each outcome of a procedure.
Probability D
4/9/15
Chapter 5
Lecture 2
Sections: 5.3 5.4
Binomial Probability Distribution
A random variable, X, is said to be Binomial if it meets the
following properties:
1. The procedure has a fixed number of trials, n.
2. Outcome of each trial must be independen
Chapter 5
Discrete Probability Distributions
Lecture 1
Sections: 5.1 5.2
Random Variables
In this chapter we will discus Discrete Random Variables
Discrete Random Variable: A random variable that assumes
values that can be counted.
n
n
n
Random Variable:
4/9/15
Chapter 4
Lecture 2
Section: 4.3
Addition Rule
We will now consider compound events. Previously we
considered simple events.
Compound Event: is any event combining two or more
simple events.
We will first look at this compound event:
P(A or B) = P(
Chapter 4
Lecture 4
Section: 4.7
Counting
Fundamental Rule of Counting:
If an event occurs m ways and if a different event occurs n ways,
then the events together occur a total of mn ways.
Example #1:
Help your girlfriend with an outfit to a summer dinner
4/9/15
Chapter 4
Probability
Lecture 1
Sections: 4.1 4.2
Fundamentals of Probability
In discussing probabilities, we must take into
consideration three things.
n Event: Any result or outcome from a procedure or
experiment.
n
Simple Event: An event that ca
Utility Table
Quantity
Consumed
Total Utility (sum of utility
from consumption)
1
2
3
4
50
90
120
140
5
6
10
150
155
160
Marginal Utility (change in
total utility divided by
change in quantity
consumed)
50
Average Utility (total utility
divided by total q
99.7% of data are Within
3 standald deviations of
the mean (,u — 30' to p. + 30')
95% within
2 standard deviations
68% within
1 standard
deviation
ILL—30' [la—20' ILL—0' ,LL “+0- “+20 ILL-F30
0.15% 2.35 %
2. 35% 0.15%
4/8/15
Chapter 3
Statistics for Describing, Exploring
and Comparing Data.
Lecture 1
Sections 3.1 3.2
n
Measure of Center
Notation:
n
Summation or addition of a set of values.
i =1
n
Number of values in a sample. (Sample Size)
N
Number of values in a po
4/9/15
Chapter 4
Lecture 3
Sections: 4.4 4.5
Multiplication Rule
In our previous lecture, we focused on P(A or B), the probability that a
trial has an outcome of A or B or both. We will now focus on
finding the P(A and B); however, differently from before
4/10/15
Chapter 6
Lecture 2
Section: 6.3
Application of Normal Distribution
In the previous section, we learned about finding the probability
of a continuous random variable. More specifically, a normal
distribution with mean equal to zero and the standar
Chapter 8
Hypothesis Testing
Lecture 1
Section: 8.2
Hypothesis Testing
We will now work with the other aspect of inferential statistics.
Previously we used sample data to make estimates, Confidence
Intervals (CI), of population parameters. We will now foc
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Ch. 7
05/11/2015
Ch. 7 Quiz Math 227
1.) Each year, millions of people take trips to theme parks owned by Disney, Universal Studios, Sea World, and
others. A survey of 1233 people who took trips revealed that 111 of th
Chapter 8
Lecture 2
Section: 8.2
Testing a Claim about a Proportion
Assumptions:
1. The sample observations are a simple random sample.
2. The conditions for a binomial distribution are satisfied.
3. The conditions np 5 and nq 5 are both satisfied.
Normal
Ch. 4
Name:
04/20/2015
Quiz 4 Math 227
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The table below summarizes results from an independent survey of 500 randomly selected college graduates who
purchased a car within one year of graduation.
Economy
Mid-Size
Luxury
Total
4/10/15
Chapter 6
Lecture 3
Sections: 6.4 6.5
Sampling Distributions and Estimators
What we want to do is find out the sampling distribution of a statistic.
Recall that a statistic is a descriptive measure about the sample. It is rare
that we know all val
Ch. 9
Name:
05/17/2015
Ch. 9 Quiz Math 227
Show all work for full credit.
1.) a. A random sample of 10 students is trying to do well on the Math assessment exam. A new training
method in order to increase scores on the Math assessment exam is given at a w
Chapter 7
Lecture 3
Section: 7.5
Estimating a Population Variance
Many real situations, such as quality control, require that
we estimate values of population variances or standard
deviations. In addition to making products with
measurements yielding a de
Ch. 10
Name:
05/17/2015
Ch. 10 Quiz Math 227
Show all work for full credit.
1.) The following data represent the number of calories per serving and the number of grams of sugar
per serving for a random sample of cereals. Answer the following problems:
Cal
Chapter 3
Lecture 3
Sections 3.4 3.5
Measure of Position
We would like to compare values from different data sets.
We will introduce a z score or standard score. This
measures how many standard deviation from the mean a
given number x is. We use the follo
4/8/15
East Los Angeles College
Math 227 - MAP
Statistics
Instructor: Gabriel Castro
Spring 2015
9:35 11:45am
Chapter 1
Introduction to Statistics
1
2
1
4/8/15
STATISTICS?
Types of Data:
n A
collection of methods for planning studies
and experiments, obta