doc - Rossman/Chance

ISCAM 3: CHAPTER 1 EXERCISES 1. Go Take a Hike!
The book Day Hikes in San Luis Obispo County by Robert Stone gives
information on 72 different hikes that one can take in the county. For each
of the 72 hikes, Stone reports the distance of the hike (in miles), the
anticipated hiking time (in minutes), the elevation gain (in feet), and the
region of the county in which the hike can be found (North County, South
County, Morro Bay, and so on, for a total of eight regions).
a) What are the observational units here?
b) How many variables are there?
c) Classify each variable as quantitative or categorical.
d) If you create a new variable that is the ratio of hiking time to hiking
distance, would that be a quantitative or categorical variable?
e) If you create a new variable called length of hike that is coded as
"short" for a hike whose distance is less than 2 miles, "medium" for a
hike whose distance is at least 2 but not more than 4 miles, and "long"
for a hike whose distance is at least 4 miles, would this be a
quantitative or categorical variable?
f) For each of the following, specify whether or not it is a legitimate
variable for the observational units you specified in (a):
. Longest hike in the book
. Average elevation gain of the hikes in the book
. Whether or not the hike is in the Morro Bay region
. Proportion of hikes with an elevation gain of more than 500 feet
. Anticipated hiking time, reported in hours
2. Identifying Variables
a) Consider the 50 states as observation units for a study. Suggest one
quantitative and one categorical variable that you could measure about
the states. (Be careful to express you answers clearly as variables.)
b) Consider the nine members of the Supreme Court as the observational
units for a study. Suggest one quantitative and one categorical variable
that you could measure about the justices. (Be careful to express your
answers clearly as variables.)
3. Bookstores
Consider all of the books in a bookstore as the observational units in a
study.
(a) Identify three quantitative variables that could be recorded on these
books.
(b) Identify three categorical variables that could be recorded on these
books.
4. Rock n' Roll
We saw a claim on "trivia coaster" from the Rock n' Roll Hall of Fame that
30% of all songs with a color in the title are about the color blue.
(a) Clearly state in words the observational units and the variable that
this claim refers to.
(b) Is the variable quantitative or categorical?
(c) Clearly state in words the population and parameter that this claim
refers to.
(d) Clearly state, both in words and in symbols, the null and alternative
hypotheses for testing the claim.
5. Predicting Elections from Faces?
Do voters make judgments about political candidates based on his/her facial
appearance? Can you correctly predict the outcome of an election, more
often than not, simply by choosing the candidate whose face is judged to be
more competent-looking? Researchers investigated this question in a study
published in Science (Todorov, Mandisodka, Goren, & Hall, 2005).
Participants were shown pictures of two candidates and asked who has the
more competent looking face. Researchers then predicted the winner to be
the candidate whose face was judged to look more competent by most of the
participants. For the 32 U.S. Senate races in 2004, this method predicted
the winner correctly in 23 of them.
a) In what proportion of the races did the "competent face" method predict
the winner correctly?
b) Describe (in words) the null model to be investigated with this study.
c) Describe how you could (in principle) use a coin to produce a simulation
analysis of whether these data provide strong evidence that the
"competent face" method would correctly predict the election winner more
than half the time. Include enough detail that someone else could
implement the full analysis and draw a reasonable conclusion.
d) Use the One Proportion Inference applet to conduct a simulation (using
1000 repetitions), addressing the question of whether the researchers'
results provide strong evidence in support of the researchers' conjecture
that the "competent face" method would correctly predict the election
winner more than half the time. Submit a copy of the applet output (e.g.,
"print screen" key or a screen capture), and indicate where the observed
research result falls in that distribution. Also report the approximate p-
value from this simulation analysis.
e) Write a paragraph, as if to the researchers, describing what your
simulation analysis reveals about whether the data provide strong
evidence in support of their conjecture.
These researchers also predicted the outcomes of 279 races for the U.S.
House of Representatives in 2004. The "competent face" method correctly
predicted the winner in 189 of those races.
f) Use the applet to conduct a simulation analysis of these data. Again
submit a copy of the "what if?" distribution, and indicate where the
observed research result falls in that distribution. Also report the
approximate p-value, and summarize your conclusion, again as if to the
researchers.
6. Can Dolphins Communicate?
A famous study from the 1960s explored whether two dolphins (Doris and
Buzz) could communicate abstract ideas. The dolphins were trained to push
the right button if a headlight was shone steadily, but the left button if
the headlight blinked on and off. Then the researcher placed a large wooden
wall in the middle of the pool. Doris was on one side of the wall and could
see the headlight, whereas Buzz was on the other side of the wall where he
could not see the headlight. When the light was shone, Doris would swim
near the wall and whistle. Buzz would then whistle back and press a button.
If he pushed the correct button (corresponding to the light Doris was
shown), they both got a fish. Dr. Bastian repeated this procedure again and
again, and Buzz pushed the correct button 22 out of 25 times. Is this
convincing evidence that Buzz and Doris could communicate?
a) Calculate the statistic for this study.
b) State the null and alternative hypotheses (in symbols and in words) to
investigate this research question.
c) Use the One Proportion Inference applet to estimate a p-value for this
significance test. Include a copy of your computer results (e.g., screen
capture).
d) Write a one-sentence interpretation of this p-value.
e) Summarize the conclusions you would draw about the research question
based on this p-value.
7. Rock-Paper-Scissors For informal sports events, players often play "rock-paper-scissors" to
decide who serves first or who is the home team etc. Two players
simultaneously show one of the three objects. The player showing the
dominant object (e.g., rock beats scissors) wins. The optimal strategy is
to alternate among the three objects. Play the game rock/paper/scissors
against the computer using the website:
http://www.nytimes.com/interactive/science/rock-paper-scissors.html. Select
the novice version of the computer to play against. Play for at least 30
rounds, but keep going for as long as you'd like. Keep track of which
option you choose (rock or paper or scissors) for every round that you play
(the computer will record this for you but that information will soon
scroll off the screen, so make your own notes). Try to recreate how you
would play against a person and don't view your prior results when making
your next selection.
a) Identify the observational units in this study.
b) Identify the variable of interest.
An article published in College Mathematics Journal (Eyler, Shalla,
Doumaux, & McDevitt, 2009) found that players tend to not prefer scissors,
choosing it less than 1/3 of the time. We will investigate whether your
data suggest that you tend to choose scissors less than one-third of the
time.
c) Calculate the statistic in this study and create a bar graph of your
results. (In R and Minitab, you can do this with just the "summarized"
data, you don't have to enter the individual outcomes.) Are your results
in the direction conjectured by these researchers (choosing scissors less
than 1/3 of the time)?
d) Define the parameter of interest in this study.
e) State appropriate null and alternative hypotheses about this parameter
according to the theory suggested in the CMJ article.
f) Explain how you could use an ordinary six-sided die to simulate a what-
if distribution under this null hypothesis. Be sure to indicate what each
possible outcome of the die (1, 2, 3, 4, 5, 6) would represent.
g) Based on your sample results, are you convinced that you choose scissors
less than one-third of the time in the long run? Clearly explain your
reasoning. 8. Which Tire?
A statistics class at Cal Poly collected data on a well-known campus
legend. Each student was asked to specify one of the four tires to answer
in a situation where you have to make up which tire had recently been flat
on your car. The prior conjecture is that a higher number than would be
expected due to chance alone would pick the right front tire. In this
class, 24 of 54 students in class chose the right front tire (a tire
identified in advance as being one that people tend to pick out of the
four). You will conduct a test of whether these data provide evidence that
Cal Poly students tend to choose the right front tire more often than would
be expected if the four tire choices were equally likely.
a) Identify the observational units and variable in this study. Also
classify the variable as categorical or quantitative. If the variable is
categorical, also indicate whether it is binary.
b) State the appropriate null and alternative hypothesis, in symbols and in
words.
c) Use technology to produce a bar graph of the student responses. Submit
this graph, and comment on what it reveals.
d) Use technology to determine the (e