Please write in the blue books provided. Show the details of your calculations. You may use a calculator, your book (including the table of standard normal probabilities and the ttable), your notes, and your homework solutions on this exam. . Notice that even though many questions contain multiple parts, you can answer later parts whether or not you correctly answer earlier parts. Also notice that some of the calculations are provided for you in many problems.
1. (20 points) A student wanted to assess whether her dog Muffin tends
to chase one of her balls more often than the other. She rolled both a
blue ball and a red ball at the same time and observed which ball Muffin
chose to chase. Repeating this process a total of 96 times, the student
found that Muffin chased the blue ball 57 times and the red ball 39 times.
a) In what proportion of the 96 tosses did Muffin chase the blue ball?
b) Is this number from a) a parameter or a statistic? Explain.
c) The student performed a significance test of
vs. , where
represents the proportion of times that Muffin would chase the blue ball
in the long run. Calculate the appropriate test statistic.
d) Determine the pvalue of the test.
e) Would you reject the null hypothesis at the .01 significance level?
f) Report the smallest significance level
at which you would reject the null hypothesis.
g) Write a onesentence conclusion to the student summarizing what
the data reveal about whether her dog Muffin tends to chase one of her
balls more often than the other.
2. (20 points) To investigate a possible relationship between heart
disease and baldness, researchers asked a sample of 663 males suffering
from heart disease to classify their degree of baldness on a fivepoint
scale. They also asked a control group (not suffering from heart disease)
of 772 males to do the same baldness assessment. The results are summarized
in the table:
none  little  some  much  extreme  
heart disease  251  165  195  50  2 
control  331  221  185  34  1 
a) Identify the cases (observational
units) in this study.
b) Is this a controlled experiment
or an observational study? if it is an observational study, what kind is
it? Explain briefly.
c) Calculate the proportion of heart
disease patients who report some or more (i.e., some, much, or extreme)
baldness. Also calculate the proportion of control group patients who report
some or more baldness.
d) Perform the appropriate test
of significance to determine if these sample proportions differ significantly
at the .05 level. State the null and alternative hypotheses in symbols
and in words, and report the test statistic and pvalue. Include a onesentence
conclusion related to the context.
e) What conclusion do you draw regarding
a possible relationship between baldness and heart disease?
3. (20 points) The following data are the prices of a sample of 41 prizes from the television game show The Price is Right:
990 999 1000 1019 1020 1078 1080 1099 1169 1169 1198
1200 1282 1325 1395 1399 1450 1482 1500 1500 1515 1539
1547 1550 1599 1600 1754 1895 1979 1995




















a) Let
represent the mean price among all prizes awarded on this game show. Use
the sample information to construct a 98% confidence interval for .
b) Without doing further calculations,
indicate whether a test of significance addressing whether the sample data
provide evidence that
differs from $1000 would be significant at the .02 level. Explain your
reasoning.
c) List the technical assumptions
which underlie the use of this confidence interval procedure. Comment on
whether the assumptions seem to be satisfied in this case.
d) What proportion of the 41 prizes
have prices that fall within the interval? Should this proportion generally
be close to .98? Explain briefly.
e) What proportion of the 41 prizes
have prices that fall within two standard deviations of the sample mean?
4. (10 points) Suppose that a television
news program conducts a callin poll about a proposed city ban on handgun
ownership, with the result that 1921 of 2372 calls oppose the ban. Suppose
further that the news anchors make the following announcement: "81% of
our sample opposed the ban, and we can be 95% confident that the true proportion
of citizens who opposing a handgun ban is within 1.6% of the sample result."
a) Explain how the station calculated
the 81% and 1.6% figures that it cites.
b) Is the station's conclusion justified?
Explain.
5. (10 points) Researchers in England gathered data to study whether Friday the 13th has an effect on people's behavior. One part of their study involved comparing the numbers of shoppers at a sample of 45 different grocery stores on Friday the 6th and then on Friday the 13th. They then calculated the difference between the number of shoppers on the 6th and the number of shoppers on the 13th at each store. These differences (subtracting in the order 6th minus 13th) are displayed and summarized by Minitab below:




















a) Write a few sentences describing
the distribution of the sample of differences. Comment specifically on
the researchers' conjecture that people alter their shopping habits on
Friday the 13th as oppposed to Friday the 6th.
b) Perform the appropriate test
of significance to assess whether the sample data support the researchers'
conjecture. Report the null and alternative hypotheses, test statistic,
and pvalue. Also write a brief conclusion summarizing your findings.
6. (10 points) The May 3, 1998 issue
of Parade magazine contains a discussion in the "Ask Marilyn" section
about baseball games in which the winning team scores more runs in one
inning than the losing team does in the entire game. Marilyn dubs such
a game a "big bang" and claims that a "big bang" occurs in 50% of all games
played. To investigate this claim, I examined the results of the 52 Major
League baseball games played on May 14, 1998 and found that a "big bang"
occurred in 18 of them.
a) One can use my sample data to
calculate a 95% confidence interval to estimate the proportion of all Major
League games in which a "big bang" occurs. The halfwidth of this interval
turns out to be .139. Is this finding consistent with Marilyn's claim that
a "big bang" occurs in 50% of all games? Explain briefly.
b) The following boxplots compare
the distributions of total runs scored between games in which a "big bang"
occurs (code=1) and games in which it does not occur (code=0). Write a
sentence or two comparing these distributions. In particular, address the
question of whether "big bang" games seem to occur more often in low scoring
games or in high scoring games.
7. (5 points) Suppose that you take a random sample of 10,000 Americans and find that 1111 are lefthanded. You perform a test of significance to assess whether the sample data provide evidence that more than 10% of all Americans are lefthanded, and you calculate a test statistic of 3.70 and a pvalue of .0001. Furthermore, you calculate a 99% confidence interval for the proportion of lefthanders in the America to be (.103,.119). Consider the following statements:
• The sample provides evidence that the proportion of lefthanders in America is much larger than 10%.
8. (5 points) Students who study a foreign language in high school tend to perform better on the verbal portion of the SAT than do students who do not study a foreign language in high school. Can one reasonably conclude from this observation that studying the foreign language causes students to improve their verbal skills? Explain.