CHAPTER 15 HOMEWORK
A study shows that there is a positive correlation between the size of a
Question hospital (measured by its number of beds) and the median number of days the
patients remain in the hospital. The reason for the positive correlation is:
A.
You can shorten a hospital stay by choosing a small hospital.
B.
Answer
Small hospitals are less expensive than large hospitals.
C.
Patients suffering from more serious illnesses are more likely to go to larger
hospitals, which may have more or better facilities for treatment.
The lengths of two bones, the humerus and the femur, in the fossils of the
extinct beast Archaeopteryx closely follow a straight-line pattern. The
equation of the least-squares line is :
Question
humerus length = -3.66 + (1.197 × femur length)
True or false: The correlation between the length of the humerus and the
length of the femur is negative.
Answer
True
False
The least-squares line for predicting school GPA from IQ score, based on a
sample of 78 students, is given as: GPA = -3.56 + (0.101 × IQ).
Question
Identify the statement that correctly interprets the meaning of slope b = 0.101,
with reference to the relationship between the two variables.
A.
Answer If the IQ score increases by 1 point, we expect the GPA to decrease by 0.101
points.
B.
If the IQ score increases by 1 point, we expect the GPA to increase by 0.101
points.
C.
If the GPA increases by 1 point, we expect the IQ score to increase by 0.101
points.
A study of class attendance and grades among first-year students at a state
university showed that, in general, students who attended a higher percentage
of classes earned higher grades. Class attendance explained 16 percent of the
Question variation in grade index among students.
What is the numerical value of the correlation between the percentage of
classes attended and the grade index?
A.
0.04
B.
Answer 0.40
C.
0.16
D.
-0.16
The data on the prices charged for a 16-ounce soda and for a hot dog at Major
League Baseball stadiums is displayed below.
Question
Team Hot Dog Soda
Angels 2.75 2.29
Astros 4.00 2.86
Braves 3.75 2.80
Brewers 2.50 2.67
Cardinals 3.00 3.14
Dodgers 3.75 2.50
Expos 1.47 2.20
Giants 3.75 3.00
Indians 2.50 3.00
Marlins 3.00 2.67
Mets 4.50 2.55
Padres 3.00 3.00
Phillies 3.25 2.40
Pirates 2.25 2.25
Rangers 2.25 2.25
Red Sox 3.75 2.86
Rockies 3.25 3.00
Royals 2.50 2.29
Tigers 1.60 2.00
Twins 3.00 2.20
White Sox 2.75 2.57
The correlation between the prices is r = 0.51.
What is the proportion of the variation in hot dog prices explained by the
least-squares regression of hot dog prices on 16-ounce soda prices?
A.
0.26
B.
Answer 0.51
C.
-0.51
D.
0.71
The correlation between IQ score and school GPA is r = 0.634. The
correlation between mileage (miles per gallon) of an automobile and its speed
(miles per hour) is 0. The correlation between wine consumption and deaths
Question
due to heart disease is r = -0.645.
Identify the set of variables that has the strongest straight-line relationship.
A.
IQ score and school GPA
Answer B.
Wine consumption and deaths due to heart-disease
C.
Mileage of an automobile and speed of the automobile
People who do well tend to feel good about themselves. Perhaps helping
people feel good about themselves will help them do better in school and life.
Raising self-esteem became for a time a goal in many schools. California even
Question
created a state commission to advance the cause. Which of the following
factors is responsible for the association between high self-esteem and good
school performance?
A.
The cause-and-effect relationship in one direction: high self-esteem
motivating to do well.
B.
Answer The cause-and-effect relationship in one direction: doing well raising selfesteem.
C.
The cause-and-effect relationship may be in both directions.
The February 2, 2008, issue of Columbus Dispatch reported about a study on
the distance to the residences of students from the campus and the average
GPA. The summary of the results is displayed.
Residence
Avg. GPA
Residence hall
3.33
Walking distance
3.16
Near campus, long walk or short drive 3.12
Within the county, not near campus
2.97
2.94
Question Outside the county
Based on this data, the association between the distance at which a student
lives from the campus and the GPA is negative. Many universities require
freshmen to live on the campus, but these data have prompted some to suggest
that sophomores should also be required to live on the campus in order to
improve grades.
Complete the following statement by choosing the appropriate option: The
data about the distance at which a student lives from the campus and the
grades of the student implies that ___:
A.
There is no association between the distance at which a student lives from the
campus and the grades of the student.
Answer
B.
There is an association between the distance at which a student lives from the
campus and the grades of the student.
C.
There is a direct cause-and-effect relationship between the distance at which a
student lives from the campus and the grades of the student.
The opening of a newspaper report about a College Board study of 15,941
high school graduates says:
Question
Minority students who take high school algebra and geometry succeed in
college at almost the same rate as whites, a new study says. The link between
high school math and college graduation is “almost magical,” says College
Board President Donald Stewart, suggesting “math is the gatekeeper for
success in college.” “These findings,” he says, “justify serious consideration
of a national policy to ensure that all students take algebra and geometry."
True or false: The positive association between taking algebra and geometry
in college and succeeding in college is most likely caused by the effect of a
third variable.
Answer
True
False
The gas mileage of an automobile first increases and then decreases as the
speed increases. The data on speed (miles per hour) and mileage (miles per
gallon) is displayed.
Speed(x) Mileage(y)
30 20
40 24
50 26
60 24
70 20
The least-squares line for predicting mileage from speed is:
mileage = 22.8 + (0 × speed)
Refer to the given scatterplot.
Questio
n
The correlation between mileage and speed is r = 0. Identify the reason why
the regression line is insignificant in predicting mileage.
A.
There is no relationship between the two variables.
Answer B.
The relationship between the two variables is not linear.
C.
The relationship between the two variables is very weak.
Drinking moderate amounts of wine may help prevent heart attacks. The data
on yearly wine consumption (liters of alcohol from drinking wine, per person)
and yearly deaths from heart disease (deaths per 100,000 people) in 19
developed countries in 2001 is displayed.
Country Alcohol from wine death rate
Australia 3.25 80
Austria 4.75 100
Belgium 2.75 60
Canada 1.50 80
Denmark 4.50 90
Finland 3.00 120
France 8.50 40
Question Germany 3.75 90
Iceland 1.25 110
Ireland 2.00 130
Italy 7.50 60
Netherlands 2.75 70
New Zealand 2.50 100
Norway 1.75 80
Spain 5.00 50
Sweden 2.50 90
Switzerland 6.00 70
United Kingdom 2.75 120
United States 1.25 120
The correlation for these variables is r = -0.645. What does this value indicate
about the direction and strength of the association between the two variables?
A.
The association is positive and moderately strong.
Answer B.
The association is negative and moderately strong.
C.
The association is negative and moderately weak.
Researchers studied the data on yearly wine consumption (liters of alcohol
from drinking wine, per person) and yearly deaths due to heart disease (deaths
per 100,000 people) in 19 developed countries in 2001. The least-squares
regression line for predicting rate of death (y) due to heart disease caused by
wine consumption (x), is: y = 115.86 - 8.05x. The correlation for the two
variables is r = -0.645. Note that both the correlation and the slope of
regression line, are positive.
Question The least-squares line for predicting school GPA from IQ score, based on 78
students, is given as: GPA = -3.56 + (0.101 × IQ). The correlation between
these variables is r = 0.634. Note that both the correlation and the slope of
regression line, are negative.
True or false: For any given data, the correlation and the slope of least-squares
regression line will have the same sign.
Answer
True
False
The least-squares line for predicting school GPA (measured on an 11-point
Question scale) from IQ score, based on a sample of 78 seventh-grade students, is given
as: GPA = -3.56 + (0.101 × IQ).
The estimated GPA of a student whose IQ score is 115 is ____.
A.
-409.3
B.
3.56
Answer C.
1.01
D.
8.055
CHAPTER 23 HOMEWORK
A researcher looking for evidence of extrasensory perception (ESP) tests 200
subjects. Only one of the subjects does significantly better (P-value < 0.01)
than random guessing.
Question
Do the results of this study provide strong evidence that this person has
ESP? Explain.
A.
Yes. The p-value is quite small for this subject.
B.
No. The p-value is too large for this subject.
Answer
C.
No. When testing 200 subjects, each using alpha = 0.01, even if all subjects
are truly "ordinary", it is expected that one or two will display statistically
significant results just by random chance.
Question
A company compares two bottle designs by placing bottles with both designs
on the shelves of several markets in a large city. Checkout scanner data on
more than 10,000 bottles bought show that more shoppers bought Design A
than Design B. The difference is statistically significant (P-value = 0.018).
What can we conclude about the strength of the preference for Design A?
A.
The magnitude of the preference for Design A is likely to be overwhelming,
given the large sample size.
B.
Answer
The difference is statistically significant, but it may not be practically
important.
C.
The difference is statistically significant and certainly practically important.
D.
The sample size is relatively small compared to the population of the city, so
we cannot be too sure of the results.
Question
Answer
As the sample size (or number of subjects in a study) increases, the margin of
error of a 95% confidence interval will increase.
True
False
As the sample size (or the number of subjects in a study) increases, then the PQuestion value will decrease, if the null hypothesis H0 is false and all facts about the
population remain unchanged as n increases.
Answer
True
False