Name…………………………………………………Lab section………………..
Exam 3, STAT2331, Spring 2012
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 brake light that has been in use a long time is known to have a mean reaction time of
0.8 seconds. A new brake light is tried out on a random sample of 50 drivers. A 95%
confidence interval for the mean reaction time for the new light (is (0.68, 0.76)
seconds. We are interested in seeing if the two lights are different in terms of mean
reaction time. Which of the following is a correct statement?
a) The null hypothesis is that the two light means are different.
b) The null hypothesis is that 
c) The alternative hypothesis is that 
d) The null hypothesis is that 
e) The null hypothesis is that 
2) Refer to question1. Which of the following is correct? (Better means shorter mean
reaction time.)
a) We will reject the null hypothesis and conclude the new light is better.
b) We will reject the null hypothesis and conclude the new light is worse.
c) We will reject the null hypothesis but cannot say if the new light is better or worse.
d) We will fail to reject the null hypothesis and conclude the new light is better.
e) We will fail to reject the null hypothesis and conclude the new light is worse.
3) Refer to question 1. Which of the following is correct?
a) We have made a Type I error.
b) We might have made a Type I error.
c) We have made a Type II error.
d) We might have made a Type II error.
e) We have made no errors.
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 4.04 years
and a 95% confidence interval was found to be 4.04 ± 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, 4.04 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 6.5 mins. A 95% confidence interval for the mean
difference in time to relief is (3.5 mins, 6.1 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) Suppose that 24 of 30 live-born cloned cattle survive to adulthood. Which of the below
is a 95% confidence interval for the true proportion (p) of live-born cloned cattle that
survive to adulthood? (Round to the nearest %.)
a)
b)
c)
d)
e)
(70%, 90%)
(79%, 81%)
(94%, 66%)
(66%, 94%)
(72%, 99%)
7) Suppose I am very concerned about Type I errors in a testing problem. Which of the
following are false statements?
a)
b)
c)
d)
e)
The significance level is the chance of a Type I error.
If I make Type I errors more likely, I will also make Type II errors more likely.
If I make Type I errors more likely, I will make Type II errors less likely.
A confidence interval of 98% will give a significance level of 2%.
I should use a high confidence level.
8) We wish to estimate a proportion p with a margin of error of 3% (plus or minus 3%)
with confidence of 95%. What sample size do we need to ensure this?
(a) 1067
(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. If a statement is sometimes true and
sometimes false, then we will call it FALSE (ie it is only true if it is ALWAYS true).
T F (a) We can use the CI formula for a proportion when n=100.
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)
10) In his first four seasons of play, a soccer player plays in 28 games and scores in 11 of
them. He averages 0.75 goals per game in these four seasons, with a standard deviation of
0.9 goals. In his next five seasons of play, he plays in 41 games and scores in 36 of them,
with an average of 2.05 goals per game, and a standard deviation of 1.2 goals.
The coach is pleased with the player’s progress, as it seems he is scoring in more games,
and maintaining a higher goals per game average.
Use an appropriate 95% confidence interval to see if you can claim the player really is
scoring more goals per game in his most recent 5 seasons, as compared to his first four
seasons.