STA 212 Assignment # 2
Question #1
How do you choose to argue? In Thinking and Reasoning (Apr. 2007), researchers at Columbia
University conducted a series of studies to assess the cognitive skills required for successful
arguments. One study focused on whether one would choose to argue by weakening the
opposing position or by strengthening the favored position. A sample of 52 graduate students
in psychology was equally divided into two groups. Group 1 was presented with 10 items such
that the argument always attempts to strengthens the favored position. Group 2 was presented
with the same 10 items, but in this case the argument always attempts to weaken the
nonfavored position. Each student then rated the 10 arguments on a five-point scale from very
weak (1) to very strong (5). The variable of interest was the sum of the 10 item scores, called
the total rating. Summary statistics for the data are shown in the accompanying table. Compare
the mean total ratings for the two groups at α = .05. Give a practical interpretation of the
results in the words of the problem.
Question #2
The placebo effect and pain. According to research published in Science (Feb. 20, 2004), the
mere belief that you are receiving an effective treatment for pain can reduce the pain you
actually feel. Researchers tested this placebo effect on 24 volunteers as follows: Each volunteer
was put inside a magnetic resonance imaging (MRI) machine for two consecutive sessions.
During the first session, electric shocks were applied to their arms and the blood oxygen level–
dependent (BOLD) signal (a measure related to neural activity in the brain) was recorded during
pain. The second session was identical to the first, except that, prior to applying the electric
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shocks, the researchers smeared a cream on the volunteer’s arms. The volunteers were
informed that the cream would block the pain when, in fact, it was just a regular skin lotion
(i.e., a placebo). If the placebo is effective in reducing the pain experience, the BOLD
measurements should be higher, on average, in the first MRI session than in the second.
a. Identify the target parameter for this study.
b. What type of design was used to collect the data?
c. Give the null and alternative hypotheses for testing the placebo effect theory.
d. The differences between the BOLD measurements in the first and second sessions were
computed and summarized in the study as follows: nd = 24, x
-
d = .21, sd = .47. Use this
information to calculate the test statistic.
e. The p
- value of the test was reported as p
- value = .02. Make the appropriate conclusion at α =
.05.
Question #3
Hygiene of handshakes, high fives, and fist bumps. Refer to the American Journal of Infection
Control (Aug. 2014) study of the hygiene of hand greetings, Exercise 7.22 (p. 409). The number
of bacteria transferred from a gloved hand dipped into a culture of bacteria to a second gloved
hand contacted by either a handshake, high five, or fist bump was recorded. Recall that the
experiment was replicated only five times for each contact method and the data used to
compare the mean percentage of bacteria transferred for any two contact methods. Therefore,
for this independent-samples design, n1 = n2 = 5. Suppose you want to estimate the difference
between the mean percentage of bacteria transferred for the handshake and fist bump
greetings to within 10% using a 95% confidence interval.
a. Define the parameter of interest in this study.
b. Give the value of za>2 for the confidence interval.
c. What is the desired sampling error, SE?
d. From the data provided in Exercise 7.22, find estimates of the variances, for the
two contact methods.
e. Use the information in parts a–d to calculate the number of replicates for each contact
method required to obtain the desired reliability. Assume an equal number of
replicates.
Question #4
Does sleep improve mental performance? Are creativity and problem solving linked to
adequate sleep? This question was the subject of research conducted by German scientists at
the University of Lübeck (Nature, Jan. 22, 2004). One hundred volunteers were divided into two
equal-sized groups. Each volunteer took a math test that involved transforming strings of eight
digits into a new string that fit a set of given rules, as well as a third, hidden rule. Prior to taking
the test, one group received eight hours of sleep, while the other group stayed awake all night.
The scientists monitored the volunteers to determine whether and when they figured out the
third rule. Of the volunteers who slept, 39 discovered the third rule; of the volunteers who
stayed awake all night, 15 discovered the third rule. From the study results, what can you infer
about the proportions of volunteers in the two groups who discover the third rule? Support
your answer with a 90% confidence interval.
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