DS350 – QUANTITATIVE METHODS FOR BUSINESS DECISIONS
FALL SEMESTER 2003
“Big Quiz” #1
Answer the following questions in the space provided. Show your work as appropriate. Relative
problem weights are given in brackets; these total 100 points. Unless the problem indicates
otherwise, use the traditional confidence level of 95% and the traditional significance level of
=.05. The word “Pledged” in front of your signature on this “quiz” shows your ongoing
affirmation to the Stetson Honor System.
Question 1 [3 points]:
Find the sample standard deviation for the following data:
826.59
302.74
918.58
421.92
309.44
428.56
129.33
[Hint: Use the built-in function on your calculator. If you don’t know how that function works,
save this problem for last.]
Question 2 [3 points]: For a normal distribution, approximately ___________% of the data are
within two standard deviations of the mean.
Question 3 [4 points]:
Alphonso Ferrabosco is conducting a hypothesis test, and computes a p-value of .42.
What conclusion should he draw?
_____ Reject the null hypothesis.
_____ Don’t reject the null hypothesis.
______ Reject the alternative hypothesis
______ Don’t reject the alternative hypothesis
Question 4 [4 points]:
Berengaria Naverre has a “not reject” result on her hypothesis test. What conclusion
should she draw?
_____
_____
_____
_____
There is enough evidence to believe her null hypothesis is true.
There is enough evidence to believe her null hypothesis is false.
There is not enough evidence to believe her null hypothesis is true.
There is not enough evidence to believe her null hypothesis is false.
Question 5 [4 points]:
Clyde Arthur Fazenbaker is conducting a hypothesis test to determine whether a coin is
fair. He has computed a test statistic of 0. What does that imply?
_____
_____
_____
_____
He got the same number of “heads” as “tails.”
He made a computational mistake, since a test statistic cannot be 0.
His null hypothesis is false.
He made a Type I error.
Question 6 [4 points]:
Dietrich Buxtehude decides to use a nontraditional significance level of =.42. Which of
the following will happen as a result?
_____ He will make more Type I errors.
_____ He will need a larger sample.
_____ None of the above.
_____ He will make more Type II errors.
_____ He will have 41 degrees of freedom.
Question 7 [4 points]:
Euterpe Waldfogel is conducting a hypothesis test to determine whether her pet wombat,
Muffy, can successfully pick stocks. What would be a Type I error, in this context?
Question 8 [26 points, divided as indicated]:
Ferdinand Walpurgisnacht is conducting a taste test to see whether people can tell the
difference between coffee and used motor oil. He has 120 participants in his study. Each
receives three unmarked glasses – two containing one liquid and one containing the other.
People are asked to identify which glass is different from the other two.
a) [6] State Ferdinand’s null and alternative hypotheses, in words and in symbols.
b) [6] Ferdinand finds that 42 of his subjects can correctly identify the glass that is different.
Compute a test statistic using Ferdinand’s data.
c) [2] What is the distribution of the test statistic here?
d) [2] What is the p-value of your test?
PICK ONE:
z
t
__________________
e) [6] What conclusion should Ferdinand draw - in statistics jargon, and in the context of the
problem?
f) [4] Is Ferdinand’s result statistically significant? Explain.
Question 9 [20 points, divided as indicated]:
Gracetta Squornshellous takes a random sample of five of the thirty students in her
Recreational Statistics class. She asks each individual the amount of time, in minutes, that was
invested in sleeping in class during the last class meeting. The data she obtained are below.
20
15
0
40
25
a) [12] Give a 95% confidence interval for the mean amount of time that class members invested
in sleep.
b) [4] Interpret this interval.
c) [4] Gracetta is unwilling to collect any more data. However, now she wants a 100%
confidence interval. Can she have a 100% confidence interval in this situation? If so, give that
interval. If not, explain why not.
Question 10 [12 points, divided as indicated]:
Horatio Wajberlinski is conducting a study to discover whether having a regular workout
affects people’s intelligence. He randomly samples 42 people who work out regularly, and
measures their intelligence, using an IQ test.
a) [4] State Horatio’s null and alternative hypotheses, in words and in symbols. (Remember that
IQ tests are calibrated to give a mean score of 100 overall.)
b) [4] Horatio’s twin brother Herkimer has used Horatio’s data to compute a 95% confidence
interval. Herkimer’s interval was 92 + 6. Should Horatio reject his null hypothesis? Explain.
Question 10 – CONTINUED FROM PREVIOUS PAGE
c) [4] Recall that Hermiker’s 95% confidence interval was 92 + 6. Does this mean that 95% of
people who work out regularly have IQ’s between 86 and 98? Explain.
Question 11 [4 points]:
Ismerelda Tempusfugit and Jubilation T. Cornpone are both conducting a campus survey.
They ask, “Is statistics your favorite class?” Each finds that 30% of their sample says “Yes.”
(The remaining students presumably are not taking statistics.) Ismerelda sampled 42 students;
Jubilation sampled 142 students. Both compute a 95% confidence interval. Whose confidence
interval will be narrower?
_____ Ismerelda
_____ they’ll be the same
_____ Jubilation
_____ we can’t tell from the information given
Question 12 [4 points]:
Keturah Binklesnert and Leonora Overture use the same data set to compute a confidence
interval on the average starting salary for statistics majors. Keturah computes an 87%
confidence interval; Leonora computes a 93% confidence interval. Whose interval will be
narrower?
_____ Keturah
_____ they’ll be the same
_____ Leonora
_____ we can’t tell from the information given
Question 13 [4 points]:
Murgatroyd Applegarth and Neldwin P. Frump both compute 95% confidence intervals
on the mean daily sales of lottery tickets at their neighborhood convenience store. Murgatroyd’s
sample mean is 4242. Neldwin’s is 2424. They both have the same sample size and standard
deviation. Whose interval will be narrower?
_____ Murgatroyd
_____ they’ll be the same
_____ Neldwin
_____ we can’t tell from the information given
Question 14 [4 points]:
Ophelia Mungbean is contemplating the karma of her t-table. She notices that, as the
number of degrees of freedom increases, the values of the t-score decrease. Briefly explain why
this happens.
DS350 – FALL 2003 – “Knowledge Festival” #1 - SOLUTIONS
1)
3)
4)
5)
6)
7)
s = 289.22
2) 95%
Don’t reject the null hypothesis.
There is not enough evidence to believe her null hypothesis is false.
He got the same number of “heads” as “tails.”
He will make more Type I errors.
Reject the null if it’s true. Say that Muffy can pick stocks, when in reality she can’t. (NOTE:
an answer of “Muffy can pick stocks but she can’t” is NOT correct. In fact, it’s a flat-out
contradiction. With Type I and II errors, the issue is that we say that things are one way,
but in reality they’re another way.)
8a) H0: People cannot tell coffee from used motor oil.  = 1/3
HA: People can tell coffee from used motor oil.  > 1/3
42
 1
120
3 = .39
8b) z 
8c) z-score
8d) p-value = .5-.1517 = .3483
1 2
3
3
120
8e) Since the p-value is “big,” Ferdinand will not reject the null hypothesis. There is not
enough evidence to demonstrate that folk can tell coffee from used motor oil.
8f) The result is not significant. Ferdinand did not reject his null.

  
  
9a) For these data, X = 20 and s = 14.58.
CI: [best guess] + [ t, 4df ] * [ sd ]
14.58
 20 + 18.1 or 1.9 to 38.1
20  (2.776) 
5
9b) We’re pretty sure (95% confident) that the mean sleep time for all statistics students is
somewhere between 1.9 and 38.1 minutes.
9c) Using only the data she has, a 100% confidence interval would be -  to +  - that is, every
single possibility.
10a) H0: Working out regularly does not affect intelligence.  = 100
HA: Working out regularly does affect intelligence.   100
(although I’m personally inclined to think  < 100 ☺)
10b) Horatio should reject the null hypothesis. The confidence interval does not contain 100 –
indicating we’re pretty sure the population mean is not 100.
10c) NO. The confidence interval indicates that the population mean is between 86 and 98. It
is not making a statement about individual members of the population.
11) Jubilation
12) Keturah
13) they’ll be the same
14) The t-distribution is an adjustment for the additional uncertainty introduced by estimating,
rather than knowing, the population standard deviation. As our sample size increases, our
estimate of the standard deviation gets more accurate – hence less need to “fudge”. Thus,
the t-score will get smaller.