Calculus for Biologists Lab
Math 1180-002
Spring 2012
Assignment #12 - Confidence Limit Fun
Report due date: Tuesday, April 17, 2012 at 9 a.m.
? Please number your responses to each problem in your write-up.
1. Include Plot 12.1 from lab 12.
(a) Why does the curve take on the value that it does for p = 1?
(b) What were your guesses for lower and upper confidence limits from these plots?
(c) Explain what these limits mean relative to the outcome n.mut.
(d) Based on your plots, is it likely or unlikely that a true mutation frequency of p = 0.3 produced the
number n.mut of mutated base pairs? Explain.
(e) Is it likely or unlikely that a true mutation frequency of p = 0.8 produced the number n.mut of mutated
base pairs? Explain.
2. Include Plot 12.2 from lab 12.
(a) Based on your Monte Carlo simulations, is it likely or unlikely that a true mutation frequency of
p = 0.25 produced the number n.mut of mutated base pairs?
(b) Is it likely or unlikely that a true mutation frequency of p = 0.5 produced the number n.mut?
(c) How do these results compare to those of the exact method?
(d) Do you think that 30 is a sufficient number of test points to accurately estimate confidence limits?
Explain.
3. Include Plot 12.3 from lab 12. How well does the normal approximation do in estimating the lower and
upper limits?
4. (a) How would you define the lower and upper 99% confidence limits for the normal approximation?
Re-define p.l and p.h in your saved lab script accordingly. Note: the text will be useful here.
(b) Change alpha to the appropriate value (reflecting the 99% confidence interval), and execute the code
from the beginning. You need only save the last plot produced (the combination plot). Include it here.
5. Discuss the advantages and disadvantages of each of the three methods you implemented in lab 12 for
finding confidence limits.
? Save your report as a .pdf file and upload it to Blackboard.
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