DS350 – QUANTITATIVE METHODS FOR BUSINESS DECISIONS
SPRING SEMESTER 2004
“Knowledge Festival” in Celebration of the Friday 13th Holiday
This exam is given under the provisions of the Honor System; the word “Pledged” before your
signature indicates your ongoing ongoing adherence to the provisions of that System.
Answer the following questions in the space provided. SHOW YOUR WORK when applicable.
Unless the problem indicates otherwise, use the traditional confidence level of 95% and the
traditional significance level of =.05. Relative problem weights are given in brackets; these
total 100 points. Enjoy!!
Question 1 [4 points]:
Alphonso Ferrabosco II is conducting a hypothesis test. He computes a p-value of .0042.
What conclusion should he draw?
_____ Reject the null. There is enough evidence to believe the null is false.
_____ Reject the null. There is not enough evidence to believe the null is true.
_____ Don’t reject the null. There is enough evidence to believe the null is true.
_____ Don’t reject the null. There is not enough evidence to believe the null is false.
Question 2 [4 points]:
Balph Snerdwell has computed a 95% confidence interval from a data set. Berengaria
Naverre has computed an 85% confidence interval, using the same data. Which of the following
is true?
_____ Balph’s confidence interval will be wider than Berengaria’s
_____ Balph’s and Berengaria’s confidence intervals will be the same size.
_____ Berengaria’s confidence interval will be wider than Balph’s.
_____ We cannot tell from the information given.
Question 3 [4 points]:
Clorinda Cragdingle decides to be somewhat nontraditional, and conducts a hypothesis
test using a significance level of =.42, rather than =.05. What does this imply about her
results?
_____ She will make more Type I errors but fewer Type II errors.
_____ She will make more Type II errors but fewer Type I errors.
_____ She will make fewer Type I errors and fewer Type II errors.
_____ She will make more Type I errors and more Type II errors.
Question 4 [4 points]:
Recall that the Literary Digest was badly mistaken in its election poll in the 1936
presidential race. What were the primary reason(s) for this error? (NOTE: there may be more
than one correct answer; check all that apply.)
_____ Their sample size was too small.
_____ They had never conducted a poll before.
_____ Their sample was not representative of the population.
_____ Many people did not respond to the survey.
_____ Many people lied when they answered the survey.
Question 5 [4 points]:
Compute a sample standard deviation for the following numbers. Show your work.
8
9
5
2
Question 6 [12 points, divided as indicated]:
Dietrich Buxtehude believes that sleeping with a statistics book under the pillow will
improve a student’s grade on the “knowledge festival.” He recruits twelve of his friends to
participate in a study. Half of them (randomly assigned) sleep with the book under the pillow;
the other half do not. He compares their average “big quiz” grades.
a) [2] This is a {pick one}
controlled experiment
observational study
b) [6] State Dietrich’s null and alternative hypotheses, in words and in symbols.
c) [4] What would a Type I error be, in this situation?
Question 7 [4 points]:
Suppose that, in the previous problem, Dietrich had computed a p-value of .42. Which
one of the following is the best interpretation of that p-value?
_____ Students score 42% higher with a book under their pillow.
_____ There’s a 42% chance that sleeping with a book under the pillow works.
_____ There’s a 42% chance that sleeping with a book under the pillow doesn’t work.
_____ Even if putting the book under the pillow doesn’t help, there’s still a 42% chance
of getting a result similar to Dietrich’s experiment.
Question 8 [4 points]:
Continuing with the same scenario as Questions 6 and 7, above: Dietrich has gotten a
p-value of .42. Is this result statistically significant? Explain.
Question 9 [4 points]:
Which of the following statements is/are true, regarding face-to-face vs. mail surveys?
(NOTE: There may be more than one correct answer; check all that apply.)
_____ Face-to-face surveys tend to have higher response rates.
_____ You get more reliable data on sensitive questions from face-to-face surveys.
_____ Costs tend to be lower in mail surveys.
_____ Face-to-face surveys generally allow a wider range of types of questions.
Question 10 [12 points, divided as indicated]:
Euterpe Waldfogel wishes to estimate the average starting salary for the hunderds of
basketweaving majors graduating from the Rollens College of Decorative Arts. She surveys a
random sample of ten recent graduates, and notes that their average starting salary was $18,400,
with a standard deviation of $2400.
a) [8] Give a confidence interval for the average starting salary for all Rollens College
basketweaving majors.
b) [4] Suppose Euterpe were to find out that Rollens College had only graduated ten
basketweaving majors in its entire history. How would this change the answer in Part A?
Explain.
Question 11 [4 points]:
Euterpe also computed a confidence interval for the mean starting salary for flycasting
majors at Rollens College. Her interval was $20,000 + $2000. Which of the following is the
best interpretation of that interval?
_____ Most (95%) of the Rollens flycasting grads have starting salaries between $18,000 and
$22,000.
_____ If she were to survey all Rollens flycasting grads, and average their starting salaries, she’d
probably (95% chance) get an answer between $18,000 and $22,000.
_____ She’s pretty sure (95% confidence) that the average starting salary for the Rollens
flycasting grads in her sample was between $18,000 and $22,000.
_____ She’s 95% correct in believing that Rollens flycasting grads have starting salaries between
$18,000 and $22,000.
Question 12 [4 points]:
Suppose, in Question 11, Euterpe were testing H0: =21,000, versus a two-tailed
alternative. Should she reject the null hypothesis?
_____ Yes
Explain.
_____ No
_____ We can’t tell from the information given.
Question 13 [26 points, divided as indicated]:
Gracetta Squornshellous notes that the Dow Jones Industrial Average has increased on
51.42% of the days since its inception. Gracetta suspects that Friday the Thirteenth is an unlucky
day in the stock market. She investigates her claim by checking whether the Dow went up or
down, on each of the last forty Friday-the-Thirteenths.
a) [6] State Gracetta’s null and alternative hypotheses, in words and in symbols.
b) [8] Gracetta notes that the Dow increased on only eighteen of the forty days in her study.
Compute a test statistic for her data. Give the p-value.
c) [2] This is a {pick one}
_____ z-score
_____ t-score
d) [6] What conclusion should Gracetta draw, in statistics jargon (reject/don’t reject) and in
context of the problem?
e) [4] Does Gracetta have a random sample here? Explain.
Question 14 [4 points]:
When is a t-score used, rather than a z-score? More importantly: Why does one use a tscore under such circumstances?
Question 15 [6 points]:
Murgatroyd Applegarth wishes to survey Stetson students on how much time they invest
in studying. Write appropriate survey item(s) for obtaining data on this research objective.
DS350 – SPRING 2004 – “BIG QUIZ” #1 - SOLUTIONS
1)
2)
3)
4)
The p-value is small, so: Reject the null. There is enough evidence … (first choice)
Balph’s CI will be wider than Berengaria’s (first choice)
More Type I errors and fewer Type II errors (first choice)
Two problems: The sample was not representative, and many did not respond (#3 and 4)
5) EITHER: The sample mean is (8+9+5+2)/4 = 6.
The sample variance is “average [squared] distance from the mean,” or
2 2  3 2  (1) 2  (4) 2
s2 
 10
3
OR: Take each data point and square it:
X
|
X2
8
|
64
9
|
81
5
|
25
2
|
4
24
| 174
1
174     24 2
4
 10
Thus the sample variance is s 2 
3
EITHER WAY, the sample standard deviation is 10 = 3.16
6a) Controlled experiment
6b) H0: sleeping with the book under the pillow doesn’t help, book = no book
HA: sleeping with the book under the pillow does help, book > no book
6c) Saying that sleeping with the book helps, when in fact it does not.
7) “Even if putting the book under the pillow doesn’t help …” (fourth choice)
8) NO. With a large p-value, we do not reject the null. “Significant” means “we rejected.”
9) All are correct EXCEPT #2 (“You get more reliable data on sensitive questions …”)
10a) 18400  2.262
2400
10
10b) No confidence interval would be needed; we would know the population mean exactly.
11) “If she were to survey all Rollens flycasting grads …” (second choice)
12) NO. She would not reject the null, because the CI indicates that it’s reasonable to
believe the population mean is anywhere between $18,000 and $22,000.
Since $21,000 is in the interval, it could plausibly be the population mean.
13a) H0: Friday the 13th is not an unlucky day,  = .5142
HA: Friday the 13th is an unlucky day,  < .5142
.45  .5142
13b) We observed 18/40 = .45. z 
  .81 . P-value = .5-.2910 = .2090
.5142 .4858
40
13c) z-score.
13d) Don’t reject the null. There’s not enough evidence that Friday 13th is unlucky.
13e) NO. No “chance mechanism” was used in the selection of her data.
14) A t-score is used when we’re doing inference on means and the population standard
deviation is estimated. It accounts for the additional uncertainty introduced by this estimation.
15) NOTE that the question asked for the survey item(s). Don’t discuss how to conduct the
survey. Instead, give the question(s) that would go on the actual survey.