Final EXAM review
It covers : Exam 1 - correlation and linear regression
Exam 2 ( I will skip Chapter 4)
Chapter 8. Confidence Intervals for the population mean (use z and t)and proportion ,
minimum sample size
Chapter 9.1 - 9.4 hypothesis tests about the
Final EXAM — review
It covers : Exam 1 ‘- correlation and linear regression
Exam 2 - normal , binomial distribution, expected value of a random variable
Chapter 8‘ s r : ' * Conﬁdence Intervals for the population mean and proportion ,
k 7_ minimum sample
Homework 2
3.102 . The following data represent the credit scores of 22 randomly selected loan applicants.
494
728
468
533
747
639
430
690
604
422
356
805
749
600
797
702
628
625
617
647
772
572
Prepare a box-and-whisker plot. Are these data skewed in any
3.4 USE OF STANDARD DEVIATION
Empirical Rule
For a bell shaped distribution approximately
1. 68% of the observations lie within one standard
deviation of the mean
2. 95% of the observations lie within two standard
deviations of the mean
3. 99.7% of the ob
Chapter 1.
1.1.What is statistics?
The field of statistics is evolving and growing in
ways few imagined even 15 years ago.
The field of statistics has been around for
centuries, yet its significance to society and the
economy is possibly greater today tha
Chapter 2.
Organizing and graphing data.
Graphing data is the first and often most
important step in data analysis
The following handout discuss common graphs
for qualitative and quantitative variables.
1
Example 1
In 1969 the war in Vietnam was at its he
Chapter 4. Probability
Remember the objective:
Population
Probability
Probability
Sample
Describe the
sample data
Compute measures of
variability
1
1. Probability and statistics are both related to a sample
and a population.
2. Probability: certain prope
Example (Inspired by past student project) Cyclists over the age
of 13 in MA do not have to wear helmets. Suppose you have data
collected based on whether or not an adult cyclist is wearing a
helmet and whether or not automobiles pass close or leave
addit
COUNTING RULE
Counting Rule to Find Total Outcomes
If an experiment consists of three steps and if the first step can
result in m outcomes, the second step in n outcomes, and the
third in k outcomes, then
Total outcomes for the experiment = m n k
Examp
Chapter 5.1-5.3
THE RANDOM VARIABLES AND THEIR
PROBABILITY DISTRIBUTIONS
Each year, the Centers for Disease Control and
Prevention recommend a flu shot for certain groups
of people who are classified as at risk for serious
complications from the most comm
5.4 Binomial probability distribution
Toss a coin 4 times.
You are interested in
the number of tails
that you can have.
You are getting
married and plan
to
have 3 children.
You
are interested in
the
number of girls
you
can have.
The statistics paper is
a
Stat 240.
Worksheet 3 Monday
1. The following are a sample of test scores from a 100-point test: 61, 50, 100, 85, 15 ,65, 75, 70 , and 90.
(a ) Construct a box-plot to display the data
(b) describe the distribution (shape, outliers)
2. Medical researchers
Stat 240.
Worksheet 3 Wednesday
1. Medical researchers enlisted 90 subjects for an experiment comparing treatments for depression. The subjects were
randomly divided into three groups and given pills to take for a period of three months. Unknown to them,
Chapter 3.1 and 3.2
Numerical descriptive measures
Graphs provide a global/qualitative description of a
sample, but they are imprecise for use in statistical
inferences.
We use numerical measures which can be calculated
for either a sample (these measures
Take Home Exam IV:
R exam over Chapters VIII, XI
1. ( 5 pts.) Suppose your data sample consists of the following scores on a history
exam:
Scores = c(28, 40,21, 26, 17 ,27, 21, 28, 36, 34, 22, 29, 40, 27, 41, 35, 33, 34, 32, 32)
You know that the populati
Stat 240 Worksheet 9 Normal distribution
Problem 1
Obtain the following probabilities for the standard normal distribution.
a. P(z > 1.86)
b P(.68 z 1.94)
.
c. P(0 z 3.85)
d P(4.34 z 0)
.
e. P(z > 4.82)
f. P(z < 6.12)
Problem 2
Problem 3
Problem 4
Problem
Chapter 6. The Normal Probability Distribution
Suppose that the birth weights of 100 babies are recorded
Recall: The total area under the histogram is 1.
A continuous random variable is usually associated with
measurement, and can take on any value in som
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
Stat 240
EXAM 2
April 9, 2015
NAME:
Discussion session (name of your TA):
.
No Talking during the exam.
Turn off / put away all cell phones.
Only the exam sheet is allowed.
You must show
Worksheet 5 solution
1.
2.
3. P(A)=0.4 , P( B)=0.7 , P(AB)=0.9
(a) Calculate the probability that both A and B occur
Since P(AB)=P(A) + P(B) P(A B) , then P(A B)= P(A) +P(B) P(AB)= = 0.4+ 0.7- 0.9=0.2
b) Calculate the probability that A occurs and B does
Supplemental Exercises Stat240
Discrete Random Variables
Exercise 1
The board of directors of a major symphony orchestra has voted to create a players
committee for the purpose of handling employee complains. The council will consist
of the president and
Supplemental Exercises Stat240
Chapter 6
Exercise 1
For a standard normal distribution with mean 0 and standard deviation equal to 1:
A) Find the following probabilities
1 ( < 1.50)
2 ( > .98)
3 ( .25 < < 1.15)
4 ( 1.15 < < .25)
5 ( .25 < < 1.15)
6 ( < 4.
Stat 240
Worksheet Sampling distribution of the sample mean (Chapter 7 part 1)
1. The amount of money spent on food per week by an American family is known to have a mean of $150 and
a standard deviation of $25
a) Suppose a random sample of 81 families is
Homework 4 additional due Thursday , Nov 3
1. An American Medical Association study showed 40 % of all Americans suffer from high blood pressure.
Suppose we randomly sample 25 Americans to determine the number of people in the sample who have high
blood p
Supplemental Exercises Stat240
Chapter 6
Exercise 1
For a standard normal distribution with mean 0 and standard deviation equal to 1:
A) Find the following probabilities
.9332
1 P( z <1.50)
1P ( z<.98 ) =1.1635=.8365
2
P( z >.98)
3
P(.25< z< 1.15)
4
P(1
Stat 240 Workshe et 10 Solution
1. The amount of money spent on food per week by an American family
is known to have a mean of $150 and a standard deviation of $25.
a) Suppose a random sample of 81 families is taken and their sample mean
expenditure is ca
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Chapter 1.
1.1.What is statistics?
The field of statistics is evolving and growing in
ways few imagined even 15 years ago.
The field of statistics has been around for
centuries, yet its significance to society and the
economy is possibly greater today tha
A. B are independent if P(AlB) = P(A) or P(BgA) = P(B) or P(AiB) = P(A) . P(B)
A, B are mutually exclusive ( disjoint) if P(AB) = 0
P(ALJB)= P(A) + P(B) P(AB) . P(A) a 1 P(A)
P(AB) = P(A|B) - P(B) or P(AB) = P(BA) - P(A)
P(AlB) = P(AB) / P(B) ifP(B).-' o
Exam 2 practice exam
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
d) Mr X is 71 inches tall .Is this unusual height?
Question 10
Question 11
Question 12
c) Three soldiers from a squadron of 12 are to b
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
Stat 240 EXAM 2 April 7, 2016
NAME:
Discussion session (name of your TA):
No Talking during the exam.
Turn off / put away all cell phones.
Only the exam sheet is allowed.
You must show a
Homework 4 additional due Thursday , Nov 3
1. An American Medical Association study showed 40 % of all Americans suffer from high blood pressure.
Suppose we randomly sample 25 Americans to determine the number of people in the sample who have high
blood p
Exam 2 practice exam solution
Question 1
Question 2
more extreme than yours.
Question 3
Question 4
Question 5
Question 9
I believe the population mean is lower than 69 inches, otherwise it would be difficult to find a sample with average 66.
Question 10
I