Assignment 2(Math 1131A)
Pr oblem512
.
: Is there a correlation between test anxiety and exam score
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performance? Data on x = score on a measure of test and y = exam score for a
sample of n=9 students are the following (the data are consistent with summary
quantities given in the paper “ Effects of Humor on Test Anxiety and Performance,”
Psychological Reports [1999]: 1203-1212):
x: 23 14 14 0 17 20 20 15 21
y: 43 59 48 77 50 52 46 51 51
Higher values for x indicate higher levels of anxiety.
a. Construct a scatterplot, and comment on the features of the plot.
b. Does there appear to be a linear relationship between the two variables?
Based on the scatterplot, would you characterize the relationship as positive
or negative? Strong or weak?
c. Compute the value of the correlationcoefficient. Is the valur of r consistent
with your answer to Part (b)?
d. Based on the value of the correlation, is it reasonable to conclude that test
anxiety caused poor exam performance? Explain.
Pr oblem5.20
: According to the article “ First-Year Academic Success: A
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Prediction Combining Cognitive and Psychosocial Variables for Caucasian and
African American Students”(Journal of College Student
Development[1999]:599-605), high school GPA(x) and first year college GPA(y)
are mildly correlated. The data, which were collected from a Southeastern
public research university, can be summarized as follows:
n=2600,  x  9620,  y  7436,  xy  27,918,  x 2  36,168,  y 2  23145
,
a. Find the equation of the least squares regression line.
b. Interpret the value of b, the slope of the least squares line, in the context of
this problem.
c. C. What first-year GPA would you predict for a student with a 4.0 high
schhol GPA?
Pr oblem618
.
: Refer to the following information on births in the United States
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over a given perion of time:
Type of Birth
Number of Births
Single birth
41,500,000
Twins
500,000
Triplets
5000
Quadruplets
100
Use this information to approximate the probability that a randomly selected
pregnant woman who reaches full term
a. Delivers twins
b. Delivers quadruplets
c. Gives birth to more than a single child.
Problem 6.20(Page 293): A mutual fund company offers its customers several
different funds; a money market fund, three different bond funds (short-,
intermediate-, and long- term0 two stock funds ( moderate- and high risk), and a
balanced fund. Among customers who own shares in just one fund, the
percentages of customers in the different funds are as follows:
Money market
20%
Short-term bond
15%
Intermediate-term bond 10%
Long-term bond
5%
High-risk stock
18%
Moderate-risk stock
25%
Balanced fund
7%
A customer who owns shares in just one fund is randomly selected
a. What is the probability that the selected individual owns shares in the balanced
fund?
b. What is the probability that the individual owns shares in a bond fund.
c. What is the probability that the individual does not own shares in a stock fund?
Problem 6.36 (Page 304): A Gallup Poll conducted in November 2002 examined how
people perceive the risks associated with smoking. The following table summarizes
data on smoking status and perceived risk of smoking and is consistent with
summary quantities published by Gallup:
Perceived Risk
Very
Somewhat
Not Too
Not At All
Smoking Status
Harmful Harmful
Harmful
Harmful
Current Smoker
Former Smoker
Never Smoked
60
78
86
30
16
10
5
3
2
1
2
1
Assume that it is reasonable to consider these data as representative of the U.S.
adult population.
a. What is the probability that a randomly selected U.S. adult is a former
smoker?
b. What is the probability that a randomly selected U.S. adult views smoking as
very harmful?
c. What is the probability that a randomly selected U.S. adult views smoking as
very harmful given that the selected individual is a current smoker?
d. What is the probability that a randomly selected U.S. adult views smoking as
very harmful given that the selected individual is a former smoker?
e. What is the probability that a randomly selected U.S. adult views smoking as
very harmful given that the selected individual never smoked?
f. How do the probabilities computed in Parts (c), (d) and (e) compare? Does
this surprise you? Explain.
Problem 6.48(Page313): Approximately 30% of the calls to an airline reservation
phone line result in a reservation being made.
a. Suppose that an operator handles 10 calls. What is the probability that none
of the 10 calls result in a reservation?
b. What assumption did you make to calculate the probability in Part (a)?
c. What is the probability that at least one call results in a reservation being
made?
Problem 6.60((Page 325): A construction firm bids on two different contracts.
Let E1 be the event that the bid on the first contract is successful, and define E2
analogously for the second contract. Suppose that P(E1) = .4 and P(E2) = .3 and
thatE1 and E2 are independent events.
a. Calculate the probability that both bids are successful(the probability of the
event E1 and E2)
b. Calculate the probability that neither bid is successful( the probability of the
event (not E1) and (not E2)).
c. What is the probability that the firm is successful in at least one of the two
bids?