1. A study of “adverse symptoms” in users of over-thecounter pain relief medications assigned subjects at
random to one of two common pain relievers:
acetaminophen and ibuprofen. In all, 650 subjects took
acetaminophen, and 44 experienced some adverse
symptom. Of the 347 subjects who took ibuprofen, 49
had an adverse symptom. We want to assess the evidence
that the two pain relievers differ in the proportion of
people who experience an adverse symptom.
Construct and interpret a 90% confidence interval for
the size of the difference.
Choose an appropriate significance level, and perform a
hypothesis test.
2. In a study of heart surgery, one issue was the effect of
drugs called beta-blockers on the pulse rate of patients
during surgery. The available subjects were divided at
random into two groups of 30 patients each. One group
received a beta-blocker; the other group received a
placebo. The pulse rate of each patient at a critical point
during the operation was recorded. The treatment group
had mean 65.2 and standard deviation 7.8. For the control
group, the mean was 70.3 and the standard deviation was
8.3.
Give a 99% confidence interval for the difference in mean
pulse rates. Interpret the confidence interval you obtain.
Is there evidence that the mean pulse rate is different for
the groups?
3. In the 2001 regular baseball season, the World Series
Champion Arizona Diamondbacks played 81 games at home
and 81 games away. They won 48 of their home games and
44 of the games played away. We can consider these
games as samples from potentially large populations of
games played at home and away.
Most people think that it is easier to win at home than
away. Perform a significance test to determine whether
this is true for the Arizona Diamondbacks.
4. LeRoy, a starting player for a major college basketball
team, made only 40% of his free throws last season.
During the summer, he worked on developing a softer
shot in hopes of improving his free throw accuracy. In
the first eight games of this season, LeRoy made 25 free
throws in 40 attempts. You want to investigate whether
LeRoy’s work over the summer will result in a higher
proportion of free throw successes this season.
5. “The nature of work is changing at whirlwind speed. Perhaps now
more than ever before, job stress poses a threat to the health of
workers and, in turn, to the health of organizations.” So says the
National Institute for Occupational Safety and Health. Employers are
concerned about the effect of stress on their employees. Stress can
lower morale and efficiency and increase medical costs. A large survey
of restaurant employees found that 75% reported that work stress
had a negative impact on their personal life. The human resources
manager of a chain of restaurants is concerned that work stress may
be affecting the chain’s employees. She asks a random sample of 100
employees to respond yes or no to the question, “Does work stress
have a negative impact on your personal life?” Of these, 68 say “yes.”
Is there evidence to conclude that the proportion for this chain of
restaurants differs from the value given for the national survey? Use
an appropriate inference procedure to support your answer.
6. National Fuelsaver Corporation manufactures the
Platinum Gasaver, a device they claim “may increase gas
mileage by 22%.” Here are the percent changes in gas
mileage for 15 identical vehicles, as presented in one of
the company's advertisements:
48.3 46.9 46.8 44.6 40.2 38.5 34.6 33.7
28.7 28.7 24.8 10.8 10.4 6.9 -12.4
Conduct a hypothesis test to check the company’s claim.
7. The Johns Hopkins Regional Talent Searches gives the
Scholastic Aptitude Test (intended for high school juniors
and seniors) to 13-year-olds. In all, 19,883 males and
19,937 females took the tests between 1980 and 1982.
The mean scores of males and females on the verbal test
are nearly equal, but there is a clear difference between
the sexes on the mathematics test. The reason for this
difference is not understood. Here are the summary data.
Group
Males
Females
mean
416
386
s
87
74
Determine if the male scores are significantly higher than
the female scores at the a = 0.01 level.
8. To help evaluate athletes coming out of college, the National Football
League annually administers the Wunderlich test to all potential players.
The test is used to measure a job candidate’s aptitude for learning and
problem solving. Many players (through their agent) will prepare for the
test, in order to earn a good score. One agent guarantees that his test
prep method is effective, and compares a practice test he gives (the
pre-test) to the actual test they are given by the NFL (the post-test)
which follows intense test prep. Is their convincing evidence here that
the test prep method of the agent is effective?
WUNDERLICH SCORES: PreTest
17
8
25
31
19
12
6
19
35
22
PostTest
21
13
24
33
16
11
8
23
36
23