Mathematics 107 - Introduction to Probability and Statistics
Fall, 2010
Dr. Evelyn C. Bailey; Dr. Edward R. Bailey; Dr. Ricardo Conceicao
Text and materials: Elementary Statistics, 11th ed., Mario F. Triola;
Calculator (TI-83, TI-83 PLUS, TI-84 or TI-84 P
Means: Confidence Intervals and Hypothesis Testing
What are Confidence Intervals?
Definitions: unbiased estimator
confidence interval
point estimate
maximum error of estimate or
margin of error (E)
Know:
* Be able to find and to interpret confidence inter
Chapter 6
m
s
- ( x- m ) 2 /2 s 2
e
y=
s 2p
The Normal Distribution
A family of curves with parameters
and
.
Properties (page 250):
Symmetric, bell-shaped, mean=median=mode.
Continuous probability distribution: y>0, area under
the curve=1.
Probabilities
Chapter 8
Hypothesis Testing:
Means
s
x- m
z=
s n
Statistical tests and /their assumptions.
Tests for means: interval or ratio data,
simple random sample
s
x - 30
is known and n m or approximately normal
t=
s/ n
distribution.
Test statistic:
is unknown an
Homework answers (even numbers) Part 3
Page 339:
2. When using 43% as the value used to estimate the percentage of the population
who would answer yes, the maximum likely difference between 43% and the true
pop
Homework for Test 3
3/4
7.2
p. 339: 1-4, 5, 7, 9, 15, 17, 21, 23, 25, 27, 29, 33, 35, 37, 41, 43
Problems in the typed notes: Proportions: Confidence Intervals
READ 8.2 BEFORE CLASS ON WEDNESDAY 3/6
Read about Hypothesis Testing in the typed notes: Propor
Math 107Q Spring 2013
Assignment 3 - Due Wednesday, March 27
REMEMBER:
You are working in groups of two or three. YOU MAY NOT DISCUSS THIS WITH
MR. OSER OR ANY MATH TUTOR OR ANOTHER GROUP. Your group needs to figure
everything out and turn in ONE write-up
Extra Review Problems 3
1.
Data was collected concerning tobacco and alcohol use in G-rated childrens animated lms. Of the 50 lms
surveyed, 34 showed some tobacco or alcohol use. Test the claim that the majority of animated childrens
movies show the use o
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of $59 plus or
.
dd up to a pretty
both skill enough
>ling studies down
lbly they have no
igures you see are
nor are all of them
to show how prevork that one over
CHAPTER
The Little Figures
That Are Not There
our skepticism on
>ublisher" in Time
"The
30
pts
1.
Math IOTQ Test 2
March 1, 2013
(100 points)
Pledged Kg %
mma 3fQ2
G- Mznp g:,;npq
Instructions: Show all work, including zwscores and graphs for normal distribution problems.
Formulas: z 2
Show the set-up for all calcrxlations.
Car speeds w
Math 107Q 7 Test 2
October 10, 2011 Pledged Q
(110 points)
Formulas: z = a: _ 'u ,u m up a : Nipq I 2 w
0
Instructions: Show all work, including graphs. Show the set-up for all calculations.
36 1. The average annual rainfall in Springeld is 50 inches. A
17
pts
Math 107Q - Test 1
September 21, 2012
(110 points)
02 = 513213 (Ml - #2
a 2 x/npq
setup for all calculations.
Formulas: p = 2[mP(m)]
P(m) = nCmpxq"m 1 = up
Instructions: Show all work. Show the
Consider the following game: A pair of 6sided dice i
Review for Test 2
Use the following data set for the problems 1 through 4.
25
49
60
68
72
33
56
63
68
73
42
58
63
69
76
45
58
64
72
82
1.
Determine whether there are any outliers in the data set. Check both denitions of outlier and show all
work.
2.
Is th
Math 107 Review for Test 1
= [xP (x)]
P (x) = n Cx px q nx
1.
2 = [x2 P (x)] 2
= np
= npq
P (x) =
e x
x!
Two fair six-sided dice are rolled. If there is (at least one) six showing on a die, you win two dollars. If the
sum of the numbers showing is fou
Review for Test 3
1.
A sample of 40 plain M&Ms has mean weight .848 grams and standard deviation .051 grams.
(a) Use a signicance level of .05 to test the claim that the mean weight of plain M&Ms is less than
.860 grams.
(b) How large a sample is needed t
H 0 : 1 12
2 (ANOVA)
3
Chapter
One-way ANOVA
1 2 (Analysis of Variance)
Test for equality of means for 3 or more samples.
1 3
2 3
Do pair-wise testing only if a significant difference is
found.
Assumptions:
interval or ratio data
independent samples
no
Chapter 13 (non-parametric tests)
Advantages and disadvantages of non-parametric tests:
(p. 636)
Disadvantages: less sensitive, less efficient
Advantages: Distribution-free, hypotheses not involving
parameters, use for nominal or ordinal data.
Wilcoxon ra
Name/Pledged_f- - v1
~-
Test 3
Math ] 07 Summer 2011
_
Three different techniques of teaching calculus needed to be compared. Three classes were
scheduled at the same time block and students were assigned randomly to each of the classes. The
three instr
23
pts
Math 107Q Test 3
April 3, 2013
(100 points)
Pledged .8
Instructions: Show all work. Show the set-up for all calculations. Show graphs.
A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had
purchased boo
NoTES
ot-J
~ Q.~e- y.
PLEDGEDj;i
Math 107
Test 3
110 points
Part I TruelFalse. If the statement is true, indicate TRUE in the blank to the left; if the
statement is false, indicate FALSE in the blank to the left AND correct the statement so
that the stat
Page 1 of 5
Mathl07 Spring 2009
Math 107
Test 3 Pledged
Print Name
-+-K-"-rut-
-r-
TruelFalse. If the statement is true, indicate TRUE in the blank to the left; if the
statement is false, indicate FALSE in the blank to the left AND correct the
statement
[20 pts}
October 29, 2012
COVER YOUR WORK.
Math 107Q - Test 3 Grade:
Pledge #
/ 110 points
SHOW SET-UP FOR YOUR CALCULATIONS.
1. A Sign on a barrel of nuts in a supermarket says that it contains 30% cashews, 30% hazelnuts,
and 40% peanuts by weight. You
Matth7 Fall 2006 Page 1 of 5
l. True/False. If the statement is true, indicate TRUE in the blank to the l ; if the statement is
false, indicate FALSE in the blank to the left AND correct the statement so that the statement
is true (30 points).
27 [1C 1)
October 24, 2011 Math 107 Q - Test 3 Grade:
/ 110 points
Pledge K 4 y '
COVER YOUR WORK. SHOW SET-UP FOR YOUR CALCULATIONS.
[25m] 1. Out of a 1000 people aged 18 to 30 years, 51% said that religion is very important to them.
Based on this survey, a po
Proportions: Confidence Intervals and Hypothesis
Testing
Definitions:
unbiased estimator
confidence interval
Critical Value (CV)
alpha, beta
hypothesis
testing hypotheses
null hypothesis
significant majority
point estimate
maximum error of estimate or
mar
Normal Probability Distribution
Definitions:
random variable
probability distribution (pdf)
Know:
* For the standard normal:
(a) Be able to read the standard normal table to find probabilities.
(b) Be able to transform a normal distribution to the standar
Discrete Probability Distributions
Definitions:
random variable
probability distribution (pdf)
sampling distribution
binomial pdf
probability histogram
expected value
rule of thumb for unusual events
Poisson pdf
Know:
* Be able to identify a pdf and expla