BIO315/G:
Biometrics
Homework Assignment 4
Spring
2007
The metabolic rates of ectothermic vertebrates are largely driven by temperature, although other factors
(e.g., activity, the size of the animal, breeding condition, or the time that has elapsed since last ingesting
a meal) exert significant effects. One measure of energy metabolism is the consumption of oxygen (the
production of heat or carbon dioxide can also be used) at rest, often called the “resting metabolic rate”
(RMR). By definition, such measurements are made on animals that are healthy, awake, unrestrained,
acclimated to the measurement temperature, and post-absorptive (i.e., they have digested and absorbed
their last meal, but are not yet starving).
Analyze the data in the “Toad Data” file on StatCrunch web site. Each value in the data set represents
the mean of five measurements of the mass-specific oxygen consumption rate in milligrams of O2
consumed per gram of body mass per day (mg O2 g-1 d-1) of southern toads (Bufo woodhousei) that were
acclimated to temperatures of 10 oC, 17 oC, and 24 oC.
1. Calculate the (arithmetic) sample means, variances, standard deviations, and the standard errors of
the means, as well as the coefficients of variation and sample sizes for each temperature. Enter your
estimates into the spaces provided in the table below.
O2 Consumption, 10 °C

O2 Consumption, 17 °C
O2 Consumption, 24 °C
x
s2
s
SEM
CV (%)
n
The StatCrunch site uses 1.96 as the multiplier when calculating 95% confidence intervals:
Temperature Sample Mean Std. Err. DF L. Limit
U. Limit
10
2.0688 0.10186645 24 1.8585579 2.279042
17
4.93 0.1743627 34 4.575652 5.2843475
24
9.856 0.57603234 29 8.677881 11.034119
2. Using the appropriate values for t, what are the 95% confidence intervals for the mean mass-specific
oxygen consumption rate at the three temperatures? What percent of the mean is each 95% CI?
Based on the confidence intervals for the means and your estimates of the coefficients of variation
for the means of the temperature groups, which temperature group seems to be the most variable?
95% CI 10 °C:
95% CI 17 °C:
95% CI 24 °C:
3. The values for skewness for the three groups are listed below. Place your estimates of the standard
error (SE) for skewness (THIS IS NOT THE STANDARD ERROR OF THE MEAN), the test
statistic (ts) used to evaluate whether the amount of skewness is significant, and the critical values for
the tests in the table below. Is there significant skewness at any temperature? In which direction?
g1
SE g1
ts
Critical value for t:
10 oC
0.861
17 oC
1.949
24 oC
0.364
BIO315/G:
Biometrics
Homework Assignment 4
Spring
2007
4. The values for kurtosis for the three groups are listed below. Place your estimates of the standard
error (SE) for kurtosis (THIS IS NOT THE STANDARD ERROR OF THE MEAN), the test statistic
(ts) used to evaluate whether the amount of kurtosis is significant, and the critical values for the tests
in the table below.Is there significant kurtosis at any temperature? If so, is the distribution leptokurtic
or platykurtic?
g2
SE g2
ts
Critical value for t:
10 oC
0.187
17 oC
5.446
24 oC
-0.758
A pharmacochemist working for a pharmaceutical manufacturing company believes that a 15-mg dose of
their, um, “performance enhancing” drug Cilantra (which increases a man’s ability to accurately throw a
football through a tire swing) should contain 35 micrograms (g) of the active ingredient, 1,2-hydroxy-ditkalene. The pharmacochemist measures a random sample of 50 doses of the drug from the
production line, and finds a mean 1,2--hydroxy-ditkalene content of 32.85 g, with a standard
deviation of 2.75 g.
5. Do the data indicate that the mean 1,2--hydroxy-ditkalene content of this sample of drug differs
from 35 g? Use  = 0.05, and be sure your answer includes: the null hypothesis and research
(alternative) hypothesis tested, your calculation of the test statistic, the critical value, and your
interpretation of the results (i.e., do you accept or reject the null hypothesis?) State what the
interpreted results mean in plain English.
After consulting with the plant engineer, the production line is altered and a new lot of Cilantra is made.
The pharmacochemist measures a new random sample of 60 doses of Cilantra from the production line,
and finds a new mean 1,2--hydroxy-ditkalene content of 35.22 g, with a standard deviation of 2.25 g.
6. Do these data indicate that the mean 1,2--hydroxy-ditkalene content of this second run of Cilantra
is greater than that of the Cilantra made by the previous method? Note: this is not another single
sample test! Also, be sure to consider whether this is a one- or two-tailed test and arrange the means
appropriately in the test statistic. Use  = 0.05, and be sure your answer includes: the null hypothesis
and research (alternative) hypothesis tested, the test statistic, the critical value, and your
interpretation of the results (do you accept or reject the null hypothesis?).
7. Do the data indicate, based on the latest sample, that the mean 1,2--hydroxy-ditkalene content of all
doses of the Cilantra is now 35 g? Use  = 0.05, and be sure your answer includes: the null
hypothesis and research (alternative) hypothesis tested, the test statistic, the critical value, and your
interpretation of the results (do you accept or reject the null hypothesis?) State what the results mean.
A herpetologist has been studying a group of 15 box turtles living in a South Carolina hardwood forest
that he has equipped with radio transmitters. For the past two years, the herpetologist has located the
turtles each week by homing in on their radio signals. When he finds them, they are nearly always buried
in a chamber (or “form”) in the leaf litter. Box turtles construct forms all year long as a protection
against predators and extreme temperatures. He records the temperatures inside and outside of the form.
During their active season, the herpetologist has noticed that the box turtles seem to dig into the litter
wherever they happen to be when the sun goes down (i.e., they do not seem to look for a particular type
of site). However, the box turtles generally overwinter in the same form from about mid-October to midMarch (and these forms are generally deeper in the litter to protect against frost).
BIO315/G:
Biometrics
Homework Assignment 4
Spring
2007
One night in April, two weeks after the turtles have emerged from their overwintering forms, a record
100-year low temperature occurs (the temperature drops to -10 °C,). The herpetologist believes that, in
contrast to their warm season behavior, the overwintering box turtles actually choose form sites that
have greater than normal above-ground temperatures. He decides to test this hypothesis by going out that
night (at 3:00 AM, ugh!) and recording the above-ground temperatures at each turtle’s current form
(Hundred-year Freeze Site, °C), as well as at the site where that turtle spent the winter (Overwintering
Site, °C). These measurements are summarized below.
Overwintering Site
Statistic (°C)
Hundred-year Freeze
Site (°C)
Overwintering Site (°C) - Hundred-year
Freeze Site (°C)
Mean
1.595
0.072
1.523
s
2.670
4.178
2.944
8. Do the data support the herpetologist’s hypothesis that the overwintering form site temperature is
greater than the random sites chosen by the turtles during their active period? Be sure to consider
whether this is a one- or two-tailed test and arrange the data appropriately to compute the test
statistic. Use  = 0.05, and be sure your answer includes:

The null hypothesis and research (alternative) hypothesis tested

Which sample means and standard deviations you used, what test statistic you used (and why), and
your calculated t-test statistic:

The appropriate critical value of t and your interpretation of the results. Do the data support the
herpetologist’s hypothesis that the overwintering form site temperature is greater than the random
sites chosen by the turtles during their active period? (do you accept or reject the null hypothesis?)