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Biostats Midterm – Take home section (Spring 2015)
1. Use the data set on worksheet cruise ship demographics in the
file 2015 midterm data.xls. Calculate summary statistics (n,
range, arithmetic mean, median, variance, standard deviation,
coefficient of variation, skewness, and kurtosis) for the age of
passengers aboard a cruise ship, showing the formulas you used
to calculate each. Then determine the appropriate bin width and
construct a histogram to display the frequency distribution of
ages.
Next, assuming that the distribution of ages is normal, calculate
the following:
P (age > 40)
P (age < 21)
P (age < 10)
P (30 < age < 50)
P (20 < age < 60)
2. During his contract negotiations, the agent for an NFL wide
receiver claims that his client is one of the most consistent
performers in the league. To back up this claim, he states that
his client has caught a pass in 38 of the last 42 games in which
he has played. Given that the league-wide probability of catching
at least one pass in a game is 0.85, the general manager of the
team is not impressed. Is the receiver’s feat particularly unusual?
Calculate (and plot) the probability of this occurrence.
3. Recently, lionfish have invaded the nearshore waters of the
Atlantic along the southeast US coast. Still, they occur in low
abundance, and finding them is rare. In surveys of the
continental shelf off North Carolina, federal fishery scientists
estimated that the average number of lionfish is 0.11 per site that
they visit during their underwater scuba surveys. As a
recreational diver, what is the probability that you would see a
lionfish on a dive this weekend? Assume that the lionfish
abundance is constant year-round. If you make a dive each
month, what are the chances that you will see a lionfish in the
next year? Please make a plot of the probability distributions
that you use.
4. Use the three columns of data on worksheet MLB pitching stats
in the file 2015 midterm data.xls. I have compiled pitching
statistics for all major league pitchers in the National League
during 2007 when pitching at home as well as on the road
(Away). For each group, only pitchers that have thrown at least
25 innings were included. The columns represent the earned run
average (ERA = runs per 9 innings) for each pitcher. Major
League Baseball claims that the historic mean ERA for pitchers is
4.00. Set up and test hypotheses to determine if home, away,
and overall ERA in 2007 conformed to history, then interpret and
explain the results of your tests. Calculate 95% confidence
intervals for each group. How many of these intervals contain a
mean ERA of 4.00?
5. Use the data on worksheet Shark litter size in the file 2015
midterm data.xls. You have gathered data on litter size for
bonnethead sharks from two different latitudes (a northern and a
southern site). The columns represent the number of pups
produced by each female shark that you sampled. You are
interested in whether or not a difference exists between latitudes.
Set up and test an appropriate statistical hypothesis that you
would use to try to answer this question. Calculate 95%
confidence intervals for each group. Do either of these intervals
contain a mean litter size of 45 pups?
6. I am interested in testing whether total prey consumption by
sea otters differs in cold water temperatures relative to some
hypothesized value. From some pilot data, I have been able to
estimate the variance at 6.4. I would like to be able to detect a
difference of about 2 grams of prey eaten per unit time.
Assuming I set my type I error rate at 0.05, what kind of sample
size do I need to achieve a power of 90%?
Suppose I can only measure prey consumption in 10 sea otters,
what will my minimum detectable difference be, assuming all else
remains the same?
Lastly, suppose I fix my minimum detectable difference at 4 and
collect data from 10 sea otters. What kind of power will I have
assuming again that my variance and type I error rate are
unchanged from above?
7. Use the data set on worksheet corpses in the file 2015
midterm data.xls. You would like to know whether there is a
difference between the rate of cooling of freshly killed corpses
versus those that were reheated (to determine if you could fool a
coroner about time of death). You tested several rats for their
cooling constant, both when the rat was freshly killed and after
the same rat was reheated. Assuming the distribution of
differences is normal, is there any difference in the cooling
constants between freshly killed and reheated rats?
8. Again, use the data set on worksheet corpses. Test the same
hypothesis as question 7, but this time assume that the
differences are not distributed normally.
9. You recently attended the Benthic Ecology Meeting with 700 of
your colleagues. Ignoring leap years, what is the probability that
no one else at the meeting shared your birthday? What is the
probability that someone else at the meeting shared your
birthday?
You are free to use Excel to make some of the calculations, but
you need to turn in a written or typed answer sheet showing your
work (the formulas you used) for each problem, along with any
plots.