MAT130 College Algebra and Trig
Project 2
Professor Rose
Discovery Activity 1: Keeping Bruin Out
Suppose you want to plant a rectangular-shaped vegetable garden, but you need to protect it from
your neighbors crazy dog, Bruin. Although Bruin is kept in a
12.A1 Gambling in ancient Rome. Tossing four astragali (shown
below) was the most popular game of chance in Roman times.
Many throws of one present-day astragalus show that the approximate probability distribution for the four sides of the
bone that can l
15.A1 IQ test scores. The IQ scores of seventh-grade girls in a Midwest school district follow a normal distribution with standard
deviation 15. The mean IQ score for an SRS of 31 seventhgrade girls in this district was 105.84. Is there evidence that
the
20.A1 Condom usage. The National AIDS Behavioral Survey interviewed a sample of adults in the cities where AIDS is most
common. This sample included 803 heterosexuals who reported having more than one sexual partner in the past year.
We consider this an S
18.A1 In an experiment with a new tranquilizer, the pulse rates (per
minute) of 12 patients were determined before they were given
the tranquilizer and again 5 minutes later, and their pulse rates
were found to be reduced on the average by 7.2 beats with
8.A1 Stratied random sample. A local youth advisory committee
is comprised of 18 youths and 6 adults. The committe needs to
select 2 adults and 6 youths for a subcommittee to meet with
the mayor to discuss renovations to the community center. This
gives e
11.A1 Weight of eggs. The weight of eggs produced by a certain
breed of hens is normally distributed with mean 65 grams (g)
and standard deviation 5 g. Think of cartons of such eggs as
SRSs of size 12 from the population of all eggs. What is the
probabili
2.A1 Heights of women. In a large city the distribution of height
for women 18 years of age or older is given in the table below.
Height (inches)
Less than 4.4
4.4 to 4.6
4.6 to 4.8
4.8 to 5.0
5.0 to 5.2
5.2 to 5.4
Count Height (inches)
5,912
22,815
28,75
3.A1 New grading system. A crazy and lazy professor has developed a new grading system to make his life easier. He gives
10% A grades, 80% B grades and 10% C grades. Last semester
students with scores less than 15 received C s and those with
scores above
1.A1 Alligator bites. Here are data on the number of people bitten
by alligators in Florida over 36 years.
Year
Number
bitten
1972
1973
1974
1975
1976
1977
1978
1979
1980
4
3
4
5
2
14
7
2
5
Year
Number
bitten
1981
1982
1983
1984
1985
1986
1987
1988
1989
1
H OW TO MAKE A SCATTERPLOT USING EXCEL
1. Open a spreadsheet and type in a title.
2. Enter the values of the x variable in a (labeled) column or row.
3. Enter the values of the y variable in a (labeled) column or row.
4. Select an empty cell in your sprea
H OW TO MAKE A HISTOGRAM USING EXCEL
1. Open a spreadsheet and type in a title.
2. Enter the values of the variable in a (labeled) column or row.
3. Enter the upper-end points of the categories or classes in a (labeled) column or row (for
example, if a ca
Yields of Wheat versus Rainfall
Rainfall
Yields
7.2
12.9
11.3
17.9
8.8
10.3
15.9
28.7
77.6
52.2
80.6
41.6
44.5
71.3
Yields of Wheat versus Rainfall
Yie lds o f Whe at ( bus he ls pe r ac re )
90
80
70
60
50
40
30
20
5
7
9
11
13
Rainfall (inches)
15
17
19
CHAPTER 3
The Normal
Distributions
Density curves
We can draw a smooth curve over a histogram to describe its shape in
an idealized way.
EXAMPLE 1 This is done on a histogram of the IQ scores of 80
seventh grade students in a rural school.
21
Now we switc
C H A P T E R 23
Two Categorical Variables:
The Chi-Square Test
Two-way tables
We have studied hypothesis testing for one quantitative variable, and
now we do this for two categorical variables. Their distribution is
usually given by means of a table, cal
CHAPTER 9
Producing Data:
Experiments
Observation versus experiment
Data is gathered in two ways: by observation and by experiment. In
the latter case we apply some treatment to the units to observe their
responses.
Subjects, factors, treatments
DEFINITIO
CHAPTER 2
Describing Distributions
with Numbers
The description of a distribution should include shape, center, and
spread. There are two main ways to measure the center of a distribution.
Measuring center: the mean
DEFINITION The mean or average of a set
CHAPTER 4
Scatterplots and
Correlation
Explanatory and response variables
Sometimes the values of a variable depend on the values of another.
For instance, the value of weight gain depends on the value of calory
intake. In such cases, the rst variable is
CHAPTER 5
Regression
Regression lines
If the points in a scatterplot are close to a line, we can draw that line
and use it to predict the value of one variable from a value of the other.
EXAMPLE 1 The point (12.9, 77.6) is an outlier in the scatterplot
of
CHAPTER 1
Picturing Distributions
with Graphs
Individuals and variables
DEFINITION
1. Population. The group of subjects (people, animals or things)
about which information is wanted.
2. Individual or Unit. An individual member of the population.
3. Variab
CHAPTER 8
Producing Data:
Sampling
Population versus sample
DEFINITION
1. A sample is a part of the population used to get information
about the whole.
2. The sampling frame is the list of units from which the sample
is chosen (ideally, the whole populati
92.283
Introduction to Statistics
Sections 205 and 206
Fall 2013
Course Policy
Instructor
Enrique A. Gonz´ lez
a
Ofﬁce: OH 428 I
Telephone Extension: 2713
E-mail: [email protected]
Office Hours
MWF 1:00–2:00
And by appointment
Notes
Students
C H A P T E R 14
Condence Intervals:
The Basics
The reasoning of statistical estimation
EXAMPLE 1 The National Assessment of Educational Progress
survey includes a short test of quantitative skills. In a recent year, 816
young men 21 to 25 years of age to
C H A P T E R 18
Inference about a
Population Mean
When is not known, we replace the quotient / n with
s
n
It is called the standard error of the sample mean.
The t distributions
In 1908, William Sealey Gosset (18761937), who worked for the Guinness brewi
C H A P T E R 15
Tests of Signicance:
The Basics
The reasoning of tests of signicance
In addition to condence intervals, a most important kind of statistical
inference consists of assessing the evidence provided by data for or
against a statement. This is