Name…………………………………………………Lab section………………..
Exam 3, STAT2331, Fall 2011
Please do all questions. Don’t forget to show all your work for partial credit.
Multiple choice (only one answer is correct for each)
1) A pain reliever that has been in use a long time takes 20 minutes on average to be
effective. A new pain reliever is tried out on a random sample of 15 patients with postoperative pain. The mean time to relief for these patients is 15.3 minutes with a sample
standard deviation of 2.5 minutes. A 95% confidence interval is to be calculated to
determine if the mean time for relief for the new painkiller is different from 20 minutes.
The confidence interval for the true mean is:
(a) (15.1, 19.1)
(b) (15, 20)
(c) (16.1, 17.1)
(d) (13.92, 16.68)
(e) (16.68, 13.92)
2) Suppose a 95% confidence interval for the true proportion (p) of people who say they
approve of Barack Obama as President is (55%, 61%). One of the below statements is
correct, please choose it.
(a) The margin of error is plus or minus 4%.
(b) If we took many, many random samples of the same size and from each computed
a 95% confidence interval for p, about 95% of these intervals would contain p.
(c) There is 95% chance that p is bigger than 55%.
(d) There is 95% chance that p is between 55% and 61%.
(e) There is 95% chance that p is between 50% and 70%.
3) A demographer, using a random sample of n = 500 people, obtained a 95 percent
confidence interval for mean age at marriage () in years for US adults. The CI was
(26.4, 27.3). If the analyst had used a 90 percent confidence coefficient instead, the
confidence interval would be:
a.
narrower and would be less likely to contain .
b.
wider and would be more likely to contain .
c.
narrower and would be more likely to contain .
d.
contain .
It may be wider or narrower, but we know it would be more likely to
e.
.
narrower but we can’t be sure if it would be more or less likely to contain
4) A study was conducted to investigate the effectiveness of a new drug for treating Stage
4 AIDS patients. A group of AIDS patients was randomly divided into two groups. One
group received the new drug; the other group received a placebo. The difference in mean
subsequent survival (those with drugs - those without drugs) was found to be 1.04 years
and a 95% confidence interval was found to be 1.04 ± 2.37 years. Based upon this
information:
a. We can conclude that the placebo is as good as the drug.
b. We can conclude that the drug was ineffective since those taking the drug lived,
on average, 1.04 years less.
c. We can conclude that there it is possible the drug was ineffective since the 95%
confidence interval covers zero.
d. We can conclude that there is evidence the drug was effective since the 95%
confidence interval does not cover zero.
e. We can make no conclusions since we do not know the sample size nor the actual
mean survival of each group
5) Suppose we are testing the effectiveness of two drugs in timely pain relief. The first
drug is tested on a random sample of patients, and has a mean time to relief of 11.3 mins.
The second drug is also tested on a random sample of patients (a different group of
patients), and results in a mean time of 4.5 mins. A 95% confidence interval for the mean
difference in time to relief is (5.5 mins, 8.1 mins). Suppose a practically important
difference is 4 mins or more. Then we can conclude;
(a) The result is statistically significant and practically significant.
(b) The result is not statistically significant, and also not practically
significant.
(c) The result is statistically significant, but not practically significant.
(d) The result is statistically significant, but we are not sure if it is
practically significant.
(e) The result is not statistically significant, and we are not sure if it is
practically significant.
6) There have been about 510 cases of H5N1 human infection (the “bird flu”) reported
worldwide in the last decade. In 303 of these cases the patients have died, a proportion of
59.4%. A 95% CI for the “true” overall proportion of deaths is
(a)
(b)
(c)
(d)
(e)
(65.3%, 53.3%)
(58.4%, 68.0%)
(55.1%, 63.7%)
(39%, 79%)
(48%, 78%)
7) In London in 1854 there was a cholera epidemic. At the time people thought that
cholera was spread through the air, whereas it is in fact spread through water. The
physician John Snow gathered data during the epidemic. He found that if people had
drunk from a particular water pump (the Broad street pump) they were more likely to
have gotten sick. In particular of 600 people he tracked down that had drunk from the
pump, 480 got sick, whereas of 480 who had drunk from other sources, only 120 had
gotten sick. Which of the following are correct statements?
(a) This is a 1 sample proportion problem.
(b) The percentage who got sick who had drunk from the broad street pump is 60%.
(c) One quarter of the people who got their water from other sources got sick.
(d) You were 4 times more likely to get sick if you got your water from the Broad
street pump.
(e) The percentage who got sick who had drunk from other sources was 20%.
8) We wish to estimate a proportion p with a margin of error of 1% (plus or minus 1%)
with confidence of 95%. What sample size do we need to ensure this?
(a) 1000
(b) 9604
(c) 2052
(d) 1692
(e) 2401
True/False
9) Each of the following statements is either True or False. Indicate which by circling the
letter T or the letter F. Do not give any explanation.
T F (a) We can use the CI formula for a proportion when n=6.
T F (b) The z* for 95% confidence and n=40 is 1.96.
T F (c) A 90% CI for a proportion p uses z*=1.645.
T F (d) If a result is known to be practically significant, then it must be statistically
significant.
T F (e) If we are not sure if we have a practically significant result or not then we know
we don’t have a statistically significant result.
T F (f) If a 95% confidence interval for a difference in means is (-4,7) this means we
have a statistically significant difference.
T F (g) Suppose a 95% confidence interval for a difference in two means is (-1, 3). You
announce that this is a non significant result, and then the data provider suggests using a
99% interval instead. You state that this is not necessary, as the result will still be
insignificant. Is this true? (Indicate T or F)