Homework 3
1. A student project investigated the time it took for 25 right-handed people to move the minute
hand on a clock using a screw action knob. There were two identical instruments, one with a
knob that worked clockwise (right-hand thread) and one that moved counter-clockwise (lefthand thread). Time (in seconds) to move the minute hand two full circles was recorded for
each subject (each subject was recorded using both instruments). The data are labeled as left
thread and right thread in the Minitab file Threads.
a.
b.
c.
d.
e.
State H 0 and H A in terms of  .
Find the test statistic (z-score or t-score)
Obtain the p-value for the test
Using α=0.05 would you reject or fail to reject the null?
State your conclusion.
2. In a study to examine whether addition of CO2 (which plants use to fuel photosynthesis)
would cause trees to grow more quickly, three pairs of plots (pairs were plots in adjacent
areas of a forest) were selected; one of each pair was randomly chosen to have extra CO2
piped into the air around the trees (an elaborate business, as you might imagine). The
response variable is the mean increase in basal area for 30 to 40 trees in each plot, measured
as percent change per year. The data are treated and untreated (in the Minitab file data
Trees)
a. State the null and alternate hypotheses.
b. Explain why the investigators would use a one-sided test.
c. Any use of the t procedures with samples of this size is risky. Why?
d. Can you think of an argument the investigators might have used to justify a t-tool?
e. Carry out a hypothesis test (use a t-test and report your conclusions).
3. Shaquille O’Neal (at the time he was a center for the Los Angeles Lakers basketball team)
was not a very good free-throw shooter. Up until the 2000 season, his career average was just
53.3%. Just before the 2000 season, he endured special coaching. In the first two games that
season, he made 26 out of 29 free throws. We will consider these to be a random sample
from the population of all throws he could make using the new technique.
a. Make a 95% confidence interval for the new proportion.
b. Based on the confidence interval is there evidence that the new technique has improved
his percentage?
4. Nicotine patches are often used to help smokers quit. Does giving medicine to fight
depression help? Of 490 volunteer smokers, 245 were randomly assigned to receive nicotine
patches and 245 received nicotine patches that also included the anti-depression drug
Buprion. After a year, 40 subjects in the nicotine-only group had abstained from smoking,
while 87 in the nicotine-plus group had done so.
a. Test, formally, whether the drug helped in smoking abstention. Be sure to state
hypotheses, obtain the p-value, and state conclusions.
b. Give a 95% confidence for the difference in proportions who quit smoking.