BIOL 300 – Biometrics
Assignment #2
Question 1 should be solved using JMP. Make sure to include any relevant computer
output when answering questions. Questions 2-4 are to be done by hand.
1. Cabbage loopers (Trichoplusia ni) are a pest in commercial vegetable greenhouses and
crucifer field crops in the lower mainland of British Columbia. The microbial insecticide
Bacillus thuringiensis (Bt) is used in greenhouses and organic field crops to control cabbage
looper populations. In 2006, cabbage loopers were collected from greenhouses and fields, reared
in the laboratory, and their offspring surveyed for resistance. Offspring fed a diet mixture with
either high or low doses of Bt. For further information see Franklin and Myers (2008).
(a) Overall the authors expected that greenhouse populations would be more resistant to Bt
than field populations due to more frequent sprays and limited dispersal. State the null
and alternate hypothesis based on the authors expectations.
(b) Within this study, researchers predicted that field populations would be susceptible to Bt.
State your null and alternate hypotheses and compare the proportion of alive and dead
individuals in the high dose treatments for the field population to the expected values.
Are field populations susceptible to Bt? (hint you will need to exclude some of the rows
to perform the appropriate statistical test)
(c) Within this study, researchers predicted that greenhouse populations would be resistant to
Bt. State your null and alternate hypotheses and compare the proportion of alive and
dead individuals in the high dose treatments for the greenhouse population to the
expected values. Are greenhouse populations resistant to Bt?
(d) Now let’s test the overall hypothesis that you stated in part 1. Compare high doses of Bt
for greenhouse vs. field populations. Is there a significant difference in the level of
resistance between these two settings? Which has the higher level of resistance?
Franklin, M. T. and J. H. Myers. 2008. Refuges in reverse: the spread of Bacillus thuringiensis resistance
to unselected greenhouse populations of cabbage loopers Trichoplusia ni. Agricultural and Forest
Entomology. 10: 119-127.
2. A large bucket is full of batteries. 40% of the batteries are Duracell brand and 60% are
Ikea brand. Not all of the batteries are new. Some of each brand are all used up and have
no power left in them. 20% of the Duracell ones are dead and 10% of the Ikea brand are
dead
(a) If you randomly select 120 batteries, how many dead batteries do you expect to
get?
(b) If you randomly select 120 batteries, what is the probability that you get no more
than 11 dead batteries?
3. In the U.S., paper currency sometimes comes into contact with drugs such as heroin,
either during drug deals and usage, or in counting machines where it wears off from one
bill to another. A forensic survey collected fifty American $1 bills and found that 11 had
measurable amounts of heroin on them.
(a) What is the best estimate of the proportion of U.S. $1 bills that have heroin on them?
(b) Make and interpret an 85% confidence interval for this estimate.
(c) Suppose that the proportion from your sample were in fact the true/population
proportion. What is the probability of getting exactly 11 $1 bills with heroin on them
when you take a random sample of 50 bills?
4. A friend of mine claims to be a psychic so I test her in the following way. I put my hand
behind my back and randomly hold out between 1-5 fingers, and ask her to guess how
many fingers I’m holding up. We repeat this 60 times and find that she guessed correctly
16 times.
(a) Test the hypothesis that she truly is psychic using a significance level of 5%.
Make sure to clearly define your hypothesis, check any assumptions you make,
report a p-value and state a conclusion.
(b) Write a short sentence stating what the p-value means in non-statistical terms, in
the context of this example.
(c) If your conclusion from part (a) were incorrect in reality, what type of an error
would you have made? State the type of error as well as what it would mean in
the context of this example.
(d) Suppose a person is not psychic and randomly guessing at the number of fingers
behind my back. Create an interval for the number or proportion of correct
guesses we would expect them to be in 95% of the time. Center this interval
around the true mean number or proportion of times we would expect them to be
correct.