Correlation
S. Soleymani
Finding correlation between two variables is a common practice in sciences and social sciences. Two
variables are correlated when there exists is an interaction or a relationship between the two. We are
mostly interested in a line
Final Guide Selected Solutions
Problem 3. The sample proportion is already given p 0.3 . To find the number of success
x np 30(0.3) 9
(a)
1. Requirements: x 9 5 and n x 21 5
2. Formula p ME p p ME , where ME z
2
p(1 p)
n
3. CI: 0.0845 p 0.516
4. Interpre
Math 227 Study Guide
S. Soleymani
Instructions and Directions:
1. Interpret each confidence interval in the context of the problem.
2. For each hypothesis test question you must set up the original and alternate hypotheses, check
requirements, indicate th
Chapter 11 Test for Independence
Name_
1. Winning team data was collected for teams in different sports with the results given in the
following table. Use a 0.05 level of significance to test the claim that home/visitor wins are
independent of sport.
Home
Math 54 Chapter 10
1.
Chantix is a drug used as an aid to quit smoking. The numbers of subjects experiencing insomnia for each
of two treatment groups in a clinical trial of the drug are given below.
Chantix
Placebo
Number in group
129
805
Number experien
Chapter 12 Answers
1. A. s1 = 3.26
s2 = 5.04
s3 = 4.82
Check that twice the smallest standard deviation is greater than the largest.
2(3.26) = 6.52 > 5.04. The data meets the necessary conditions.
B. ANOVA table:
Between or
Factor
Within or
Error
Df
2
SS
S. Soleymani
Math 52
Percentiles and Outliers
Consider the following data set:
38
41
43
44
44
45
47
48
51
52
57
57
58
62
68
79
85
98
100
The histogram below suggests that the distribution of the data is right or positively-skewed.
Histogram
6
4
Frequency
ANOVA
Math 54
S. Soleymani
1. The L.A. Clippers and L.A. Lakers are basketball teams. On each team, the shortest player is
about 6 feet tall and the tallest player is about 7 feet tall. Consider the heights of the following
pairs of groups of people:
I.
p
Math 54 - Tables & Graphs
Names_
The table below gives the number of female job-seekers in a sample by age.
Use full sentences in all explanations.
Number of unemployed female job-seekers,
by age group
Age group *
Number of females
15 to 24
339
25 to 34
2
Chapter 12 problems Answers
1. a. There seems to be a positive trend, possibly linear and no apparent outliers.
1237.6
b. r = 0.709, y = + 7.07 x
c. The value of r indicates a strong linear correlation since r > 0.7.
d. Slope: For each increase of $1 in
Basics of Hypothesis Testing
Sam Soleymani
Hypothesis testing is a procedure to test a claim about a population parameter such as
proportion. The coin example will be used to demonstrate the reasoning behind the method of
hypothesis testing.
Outcomes of H
Frequency Tables and Histograms
Consider the data set
4
15
4
15
10
15
11
16
12
16
12
18
12
18
12
20
12
20
12
20
12
20
14
20
14
20
14
24
14
24
15
24
15
25
15
26
15
28
15
30
To construct a frequency table first determine the number of classes to be used. Th
Statistics
S. Soleymani
Probabilistic Math vs. Deterministic Math
The perception of mathematics differs among individuals. Usually our opinion of math is based on
our personal experiences and our exposure to it. Some view math as a language complex enough
S. Soleymani
CI Estimate
One Sample
,
Sample Size
Hypothesis Test
Binomial Counts
Proportions
CI Estimate
Two Samples
Hypothesis Test
,
S. Soleymani
CI Estimate
One Sample
Sample Size
Hypothesis Test
Continuous Measures
Averages
CI Estimate
Two Independen
Simple Linear Regression Analysis
L
Math 54
S. Soleym
mani
The Cou
unter Crime Unit reports the number of homicid that have occurred l month v
U
s
r
des
e
last
versus
the perce
entage of hou
useholds ow
wning a licens gun.
sed
City
Percentage of Household
S. Soleymani
One-Population Proportion Hypothesis and Decision Analysis
Cell Phones and Cancer In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of
the brain or nervous system (based on data from the Journal of the National Canc
Math 54
S. Soleymani
Expectation and Variation
As mentioned earlier, in probabilistic mathematics and statistics outcomes of an experiment cannot
be predicted with 100% certainty due to randomness. To wrap your mind around this notion let us
compare a det
More about Inferential Statistics
First few topics in elementary statistics courses solely focus on descriptive statistics, such as frequency
distributions, measure of center, spread, and position. Thereafter, the focus is shifted to the notion of
probabi
1f. Suppose that 27% of all students at a particular community college take the bus to
school. What is the probability that a sample of 15 students will contain between 5 and 11,
inclusive, students who take the bus to school?
4b. Suppose that a batch of
Chapter 13
Name_
The table below gives the High school and college GPA for 10 students.
H.S. GPA
(x)
College
GPA (y)
2.4
2.5
2.9
2.7
3.0
3.5
3.0
3.6
3.4
3.9
2.6
1.9
2.7
2.5
2.4
2.9
2.7
3.1
3.0
3.3
1. Draw a scatterplot for this data set and answer the thr
Math 54 Sampling Distributions of the mean and Central Limit Theorem 19 points
Names_
The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.
a. If one pregnant woman is selected, find the probabili
Section 3.4 Measures of Position
How individual data points are positioned within a data set.
Percentiles
Pk is the value such that k% of a data set is less than or equal to Pk.
For example if we said that on a recent Math SAT exam, P89 = 660, then 89% of
Math 54 Correlation
Names_
The following table gives the cost (per serving in $) and the sodium content (per serving in mg) for 7
different brands of frozen enchiladas.
Brand and Type
Amys Black Bean
Patio Cheese
El Carrito Beef
Banquet Cheese
Healthy Ch
Math 54 chapter 3
Name_
The extra time that a commuter spends travelling per year due to traffic congestion was measured for a
sample of 14 cities. The results listed below are given in extra hours per year.
98
50
75
43
66
22
65
64
61
55
54
48
53
46
a. Fi
Names_
NORMAL PROBABILITY DISTRIBUTION
In this project your group will be working for an apparel company that makes blue jeans. They are trying
to determine some information about the heights of women to make decisions about sizing for their
products.
To
Math 54 - Review - Chapter 1 - 9 (not including ch. 4)
You may use posted problem sets and the text book to review more recent material.
1. Identify the level of measurement (nominal, ordinal, interval, ratio) used in each of the following.
a. the weight
Names_
1. Draw and find the indicated standard normal probabilities using the appropriate table.
a. P(z > -1.47)=_
b. P(-2.01 < z < 1.05)=_
c. P(z < 0.68) = _
d. P(z > 4.03) = _
e. P(1.25 < z < 3.02) = _
Using the table, find the value of z from the given
Name(s):
The New York State Health Department reports a 10% rate of the HIV virus for the atrisk population.
1. If 12 members of the at-risk population are randomly selected, what is the
probability that exactly 3 of them will have the HIV virus? Use the
Chapter 12 ANOVA Analysis of Variance
1. The data below represent the number of pods on a random sample of soybean plants for three
different plot types. An agricultural researcher wants to test the claim that the mean number of
pods for each plot type ar