MATH 1342.01
Test 2
6/27/16
Name
This test has 25 problems, each worth 4 points. Questions marked (MC) are multiple choice;
circle the letter that best answers the question. In questions marked supporting work required,
credit is based on the completeness
Section 2.2 SOME GRAPHICAL DISPLAYS OF DATA
Bar graphs and circle graphs are two ways to represent qualitative data in
graphical form.
EXAMPLE 1. The table below contains the lab grades of 200 lab students.
a.
Complete the table.
The relative frequency o
31 DISTRIBUTION OF THE SAMPLE MEAN AND THE CENTRAL LIMIT
THEOREM
Given a population (called the parent population), we will pick randomnN-lii: X
samples of n items (with replacement) and compute their sa_mple means.
We would like to study the distributio
30 STANDARDIZING ARBITRARY NORMAL DISTRIBUTIONS
If X is a normal variable with mean u and standard deviation a, then X can
be converted into a standard normal variable Z using the formula
X - I1
U .
When given a value of X, the corresponding value of Z is
39 CONFIDENCE INTERVAL FOR THE POPULATION MEAN WHEN THE
POPULATION STANDARD DEVIATION IS UNKNOWN
We now consider a population that is normally distributed but in which the
population standard deviation 6 is not known. In this case. we will use the
point e
32 APPLYING THE CENTRAL LIMIT THEOREM
if the sample size n is large (n > 30) or if the parent population is normally
distributed, then distribution of
: X _ i
i
is close to that of the standard normal variable Z and so we can then use the
formula ,Mt
29 THE STANDARD NORMAL DISTRIBUTION
The most important continuous distributions used in statistics are called
normal (or Gaussian) distributions and are characterized by the following
properties:
0 Each normal distribution is described by a smooth bell-sh
15 PROBABILITY IN EQUALLY LIKELY SAMPLE SPACES
A sample space for an ex
_ periment is the set of all possible outcomes. An
equally likely sample spa
ce is a sample space in which each outcome has
an equal chance of occurring. For example. for an experimen
23 THE BINOMIAL DISTRIBUTION :. {Merrie
I.
A binomial experiment consists of a xed number of independent and
identically performed trials each of which results in an outcome of success
or failure. Moreover, the probability of success on each trial is know
ESTIMATING THE POPULATION
PROPORTION
(1a)100 percent condent that the
A sample size n needed so as to be
population Man p by more
sample proportion p' is not in error of the
than a quantity E is given by
2 - .
it n = [2632)] prqt W
where p" and q* are pro
17 PROBABILITY IN GENERAL SAMPLE SPACES
Given a nite sample space, a valid probability assignment must assign a
probability to each outcome in the sample space so that
o the probability of each outcome must be a number between 0 and 1,
inclusive; and
o th
6 SUMMATION NOTATION a. l
o-i
Given n data values denoted x1. X2. x. the symbol Ex is'an abbreviation
for the sum
X1+Xz+ +Xn.
EXAMPLE 1. Consider the following'ugvizrjate data set:
6, 3, 2, 9
Find the value of each of the following.
If?
a. n
b. Ex myth{3
\
" KIN-tire!
7 MEASURES OF CENTRAL TENDENCY
Given a set of data values, we wish to nd a single number that somehow
measures the center of the data. The value of a measure of central
tendency can be positive, negative, or zero; however. this value should
9 MEASURES OF POSITION
Given a data set ordered from smallest to largest, the kh percentile, denoted
by Pk. is a value such that at most k% of the data values he below this value
and at most (100k)% of the data values Iie above this value.
We of the data
21 MULTIPLICATION RULE 0F PROBABILITY
From the conditional probability formula in the previous section. we get the
General Multiplication Rule:
P(A and B) = P(A)-P(BIA) = PiB)-P(AIB)
EXAMPLE 1. Suppose E and F are two events such that P(E|F) = 0].
PE) = 0
5 MISUSES OF STATISTICS
EXAMPLE 1. Consider the following article.
Males Out Number Females at Eastern High School
A recent report to the school
board stated that the number of
male students has increased
over the previous year. It also
mentioned that for
9 MEASURES OF POSITION
Given a data set ordered from smallest to largest, the kh percentile, denoted
by Pk. is a value such that at most k% of the data values he below this value
and at most (100k)% of the data values Iie above this value.
We of the data
13 LINEAR REGRESSION
We now consider bivariate data (data consisting of ordered pairs of numbers)
and are interested in whether the data resembles a line or not. The following
steps will be used:
- Plot a scatter diagram of the data.
Compute the linear co
4 FREQUENCY DISTRIBUTIONS. HISTOGRAMS. AND OGIVES
EXAMPLE 1. The following raw data was obtained when a die was rolled
twenty times.
14151136436543341216
Complete the following ungr0uped frequency table.
Number 3: Tally Frequency f
1 Mi (0
2 | I
3 in! l
4
23 INDEPENDENT EVENTS
Let A and B be events which are not impossible. Then the following are
equivalent (all true or all false):
' P(AIB) = P0)
° P(BIA) = P(B)
- P(A and B) = P(A)-P(B)
Two events A and B are said to be independent if any of these three
eq
. ,s
as
34 INTRODUCTION TO CONFIDENCE INTERVALS
Another method of estimating a parameter is the method of condence
intervals. Stated with a specified level of condence, a confidence Interval
provides an interval of numerical values that is believed to con
PM) :
i(.rr+-°i3:
26 DISCRETE RANDOM VARIABLES
Let X be a discrete random variable taking on the values x1, X2, .
P is a probability function for X if P is a function from {X1. X2. .
real numbers satisfying:
., X". Then
. xn} into the
o for all i, 0 s P
12 GROUPED DATA
Given a data set consisting of X1. x2, Xi; having respective frequencies
2, f2, ft. the sample size, sample mean and sample variance are given
if
n = 2f
2 : :3
n
and
= 8800
n1
52
where 830:) = ZxE)? = foz _ (Em)
n
Note: If the data set
48
TW
For hypothesis tests involving Di. ._p
where p;, the pooled observed probability, is given by p; =
1'" I
I} n; : _"
ise a'J 3'15
' 0W *5. >
HYPOTHESIS TEST FOé THE DIFFERENCE BETWEEN
PROPORTIONS USING INDEPENDENT SAMPLES
\useth test stati
19 ADDITION RULES OF PROBABILITY
In mathematics, or means "and/or." For instance. "A or 8" means A or B
or both. In this sense, "or" is said to be inclusive. For two events A and B,
the probability that A or B occurs is given by the General Addition Rule: