What preys on the peppered moth

Introduction
This assessment is given strictly as a means of evaluating student learning accomplishments in this course. I expect students will approach this exam in much the same way they would approach any exam: do their best.
Three important points before you begin: first please answer the questions where the highlighted cell is located. This will facilitate grading. Second, you are not required to perform any analyses, but this doesn't mean you are disallowed from performing any analyses.
Third, use your name (last, first) as the file name for this document when you turn it in.
q1
The peppered moth (Biston betularia) occurs as two phenotypes: peppered (speckled black and white) and melanic (black).
A researcher wished to measure the proportion of melanic individuals in the peppered moth population in England, to examine how this proportion changed from year to year in the past.
To accomplish this, she photographed all the peppered moth specimens available in museums and large private collections and grouped them by the year in which they had been collected.
Based on this sample, she calculated the proportion of melanic individuals in every year.
The people who collected the specimens, she knew, would prefer to collect whichever type was rarest in any given year, since those would be the most valuable.
Can the specimens from any given year be considered a random sample from the moth population?
If not a random sample, what type of sample is it? What type of error might be introduced by the sampling method when estimating the proportion of melanic moths?
q2
The accompanying graph indicates the amount of time (latency) that female subjects were willing to leave their hand in icy water while they were swearing
(“words you might use after hitting yourself on the thumb with a hammer”) or while not swearing, using other words instead (“words to describe a table”). The data are from Stephens et al. (2009).
What type of gragh is shown here?
Why it is it appropriate for depicting the data that were collected?
What do the "whiskers" indicate on this graph?
List one other type of graph that would be appropriate for illustrating these results.
What can you infer about swearing from this graph?
q3
When a female jewel wasp (Ampulex compressa) encounters a cockroach (Periplaneta americana),
she stings and injects neurotoxins into its head that render the insect unable to initiate self-movement but not paralyzed.
The wasp then holds the compliant (zombie) cockroach by the antenna and leads it to her nest, where it will become live food for her larval offspring.
The following graph (data from Gal and Libersat 2010) compares the mean self-initiated walking duration of stung and control cockroaches during the first 30 minutes after treatment. The error bars indicate approximate 95% confidence intervals; n = 5 in each group.
What type of graph is this?
What is the approximate value of the standard error for the control group
List one other type of graph that could be used to depict these data.
What can you infer about cockroach behavior after being stung?
q4
The following table was compiled by the U.S. Social Security Administration (2018) and the U.S. Census Bureau (2018).
It lists the annual probabilities of death for U.S. residents in their early 20s according to gender (as defined by these U.S. government agencies).
How would you calculate the probability that a randomly chosen male 20 to 15 years old is male?
How would you calculate the probability of death for a randomly chosen 20 to 24 year old American?
q5
A team of researchers conducted 100 independent hypothesis tests using a significance level of α = 0.05.
If all 100 null hypotheses were true, what is the probability that the researchers would reject none of them?
If all 100 null hypotheses were true, how many of these tests on average are expected to reject the null hypothesis?
q6
Some people have suggested that Alzheimer disease may be at least partially caused by a contagious agent.
If this were true, one might expect that people who come into contact with brain tissue may be more likely to be exposed to such contagion.
Lollis et al. (2010) found that 14 of 7163 male neurosurgeons contracted Alzheimer disease during a 26-year study.
The probability of Alzheimer disease in the general population of males of the same age group is 0.00084.
How would you determine the 95% confidence interval for the proportion of neurosurgeons who contract Alzheimer disease.
q7
The National Electronic Injury Surveillance System (Consumer Product Safety Commission 2018) recorded the number of injuries associated with computers and video games.
A sample of these injuries (all severe enough to merit admission to an emergency room) is recorded in the table below, according to the day of the week of the admission.
Describe what you would do to test whether hospital admissions occur with equal probability on each day of the week. Assume that each day has the same frequency of occurrence over the time interval investigated.
q8
Cummings et al. (2003) estimate that the relative risk of death in a vehicle crash for occupants 16 to 34 years old who were wearing a seatbelt was 0.36 compared to those not wearing a seatbelt. Interpret this statement.
q9
The crab spider, Thomisus spectabilis, sits on flowers and preys upon visiting honeybees.
Do honeybees distinguish between flowers that have crab spiders and flowers that do not?
To test this, Heiling et al. (2003) gave 33 bees a choice between two flowers: one had a crab spider and the other did not. In 24 of the 33 trials, the bees picked the flower that had the spider.
In the remaining nine trials, the bees chose the spiderless flower.
With these data, what appropriate hypothesis test would you use to calculate P?
q10
Two different researchers measured the weight of two separate samples of ruby-throated hummingbirds from the same population.
Each calculated a 95% confidence interval for the mean weight of these birds.
Researcher 1 found the 95% confidence interval to be 3.12 g < μ < 3.48 g , while Researcher 2 found the 95% confidence interval to be 3.05 g < μ < 3.62 g .
Provide at least two reasons why or how could the two researchers get different answers?
Which of your reasons can you be certain about in your answer above?
q11
The males of stalk-eyed flies (Cyrtodiopsis dalmanni) have long eye stalks. The females sometimes use the length of these eye stalks to choose mates.
Is the male’s eye-stalk length affected by the quality of its diet?
An experiment was carried out in which two groups of male “stalkies” were reared on different foods (David et al. 2000).
One group was fed corn (considered a high-quality food), while the other was fed cotton wool (a food of substantially lower quality).
Each male was raised singly and so represents an independent sampling unit. The eye spans (the distance between the eyes) were recorded in millimeters. The raw data, which are plotted as histograms at right, are as follows:
mean(mm) standard deviation (mm) variance (mm^2) Sample size, n
Corn diet (group1) 2.05 0.0746993976 0.00558 21
Cotton diet (group2) 1.54 0.284956137 0.0812 24
What is the best statistical test to use for comparing the means of these two groups? Why?
food eyeSpan
Corn 2.15
Corn 2.14
Corn 2.13
Corn 2.13
Corn 2.12
Corn 2.11
Corn 2.1
Corn 2.08
Corn 2.08
Corn 2.08
Corn 2.04
Corn 2.05
Corn 2.03
Corn 2.02
Corn 2.01
Corn 2
Corn 1.99
Corn 1.96
Corn 1.95
Corn 1.93
Corn 1.89
Cotton 2.12
Cotton 2.07
Cotton 2.01
Cotton 1.93
Cotton 1.77
Cotton 1.68
Cotton 1.64
Cotton 1.61
Cotton 1.59
Cotton 1.58
Cotton 1.56
Cotton 1.55
Cotton 1.54
Cotton 1.49
Cotton 1.45
Cotton 1.43
Cotton 1.39
Cotton 1.34
Cotton 1.33
Cotton 1.29
Cotton 1.26
Cotton 1.24
Cotton 1.11
Cotton 1.05
q12
Dormant eggs of the zooplankton Daphnia survive in lake sediments for decades, making it possible to measure their physiological traits in past years.
Hairston et al. (1999) extracted Daphnia eggs from sediment cores of Lake Constance in Europe to examine trends in resistance to dietary cyanobacteria, a toxic food type that has increased in density since 1960 in response to increased nutrients in the lake.
The data and accompanying histogram give the resistance level of 32 Daphnia clones, each initiated from single eggs extracted from deposits laid down during years of low, medium, and high cyanobacteria density between 1962 and 1997.
Resistance is the average growth rate of individuals fed cyanobacteria divided by the growth rate when individuals from the same clone are fed a high-quality algal food instead.
We wish to test whether resistance differs among Daphnia clones from the three cyanobacteria density groups.
Examine the histograms of the data.
Give two reasons why caution is warranted before using ANOVA to test for differences among group means in this case.
The data were analyzed using a Kruskal–Wallis test. What are the null and alternative hypotheses for this test? The results of the test were as follows: H = 8.20 . What is the conclusion?
Under what assumption would we be able to use the results of the test to draw a conclusion about whether the means or medians are the same in the three groups? Is this assumption met here?
cyandensity resistance
high 0.65
high 0.73
high 0.74
high 0.76
high 0.81
high 0.82
high 0.85
high 0.86
high 0.88
high 0.9
med 0.7
med 0.74
med 0.75
med 0.76
med 0.78
med 0.79
med 0.8
med 0.82
med 0.83
med 0.86
low 0.56
low 0.57
low 0.58
low 0.62
low 0.64
low 0.65
low 0.67
low 0.68
low 0.74
low 0.78
low 0.85
low 0.86
q13
Cocaine is thought to affect the brain by blocking the dopamine transporter, increasing the amount of dopamine in the nerve synapse.
To investigate this idea, Volkow et al. (1997) administered intravenous doses of 0.3 to 0.6 mg/kg of cocaine to volunteers.
They used PET scans to compare the magnitude of the perceived “high” of regular cocaine users with the percentage of dopamine receptors blocked. The results for 34 subjects are illustrated below.
Estimate the correlation between the percentage of dopamine receptors blocked and subjects’ ratings of the cocaine high.
What are your assumptions?
Imagine the following scenario: A second team of researchers carried out a similar study using the same population and sample size.
They used a narrower range of intravenous doses of cocaine in their experiment, which led to a smaller range of values than in the first study for the percentage of dopamine receptors blocked.
When they analyzed their results, they found only a low correlation between percentage dopamine receptors blocked and perceived high.
In their published report, they concluded that the true correlation between these variables is much lower than estimated in the Volkow et al. study. Who is right? Explain.
percentBlocked high
70 10
71 10
82 10
88 10
46 8
66 8
68 8
83 8
40 7
65 7
48 6
63 6
74 6
41 5
43 5
46 5
58 5
67 5
90 5
32 3
63 3
65 3
68 3
40 2
41 2
59 2
34 1
38 0
42 0
45 0
52 0
56 0
57 0
60 0
q14
In promiscuous species of mammals, such as deer mouse, the breeding success of males can be predicted from their testes size and the number of sperm they produce.
Fisher et al. (2018) investigated whether testes size could be affected by the intrauterine environment of fetal mice.
In particular, they examined whether the number of male littermates could predict male testes size. (Such an association might occur, for example, if many males in a litter generated a higher-testosterone environment for all developing embryos.)
The data are shown in the figure below.
Do these data fit the assumptions of linear regression well? Explain.
Given the best-fitting line predicting testes area from the number of male littermates. Do these data provide sufficient evidence that testes area is predictable from the number of male littermates?
TestisArea_mm2 NumMaleLittermates NumFemaleLittermates LitterSize Weight_g
MaleID 32.8 3 0 4 14
HF317 34 3 0 4 15.8
HF316 21.46666667 1 0 2 11.6
HF325 36 0 1 2 16.3
HF337 36.53333333 1 1 3 18.5
HF338 27.86666667 2 0 3 12.9
HF346 35.73333333 3 0 4 12.6
HF318 31.33333333 2 0 3 14.6
HF348 30.53333333 0 3 4 13.7
HF349 36.53333333 0 0 1 18.2
HF330 29.73333333 0 3 4 16.9
HF309 31.2 0 3 4 18.6
HF342 32.13333333 3 0 4 20.5
HF407 29.2 1 1 3 15.5
HF304 34.13333333 1 0 2 16.2
HF324 34 1 2 4 18
HF376 32.26666667 0 1 2 14.9
HF385 36.93333333 3 0 4 15.8
HF406 31.86666667 0 2 3 13.2
HF375 32 1 0 2 17.8
HF411 27.86666667 1 2 4 16
HF422 29.06666667 1 3 5 18.2
HF418 32 1 2 4 22.2
HF423 28.53333333 3 1 5 13.4
HF427 33.2 2 1 4 10.4
HF445 25.2 2 0 3 14.8
HF439 34.53333333 2 0 3 18
HF487 17.86666667 2 0 3 18.1
HF488 27.33333333 0 3 4 15.1
HF441 25.2 2 0 3 13
HF521 37.06666667 3 1 5 14.9
HF506 27.2 3 1 5 18.4
HF507 31.06666667 1 1 3 13
HF512 35.06666667 1 0 2 17.4
HF514 29.86666667 0 1 2 21.4
HF545 31.73333333 2 0 3 20
HF548 45.06666667 4 1 6 12.1
HF555 35.6 4 1 6 13.4
HF552 29.2 0 2 3 12.9
HF565 28.26666667 1 2 4 16.7
HF562 37.73333333 3 2 6 14.2
HF571 26.26666667 1 2 4 18.4
HF580 29.86666667 4 1 6 14.6
HF598 38.93333333 4 1 6 10.7
HF601 33.6 1 1 3 13.2
HF615 33.86666667 0 3 4 12.3
HF625 24.4 2 3 6 19.1
HF635 28.4 0 3 4 14.8
HF629 23.86666667 1 2 4 12.7
HF639 32.8 2 3 6 11.2
HF633 36 1 1 3 16.9
HF678 31.33333333 0 1 2 19.2
HF680.5 28.4 3 0 4 20.8
HF673 32.53333333 3 2 6 11
HF680 27.46666667 3 0 4 12.1
HF674 41.2 3 2 6 17.5
HF681newgeno_682pheno 37.86666667 2 0 3 15.7
HF684 42 2 0 3 17.3
HF686 35.06666667 2 0 3 13.8
HF687 36 1 1 3 15.6
HF679 42.66666667 3 2 6 15.6
HF681ori 26.26666667 1 0 2 14.7
HF815 23.73333333 2 3 6 17.5
HF821 28.53333333 1 2 4 14.1
HF809 23.46666667 3 0 4 13
HF797 22.26666667 0 3 4 12.4
HF849 19.73333333 0 4 5 17.8
HF854 41.2 2 1 4 16.8
HF866 27.33333333 2 2 5 16.3
HF869 24.53333333 2 3 6 18.7
HF881 22 3 1 5 28.4
HF885 31.33333333 1 2 4 17.1
HF894 27.73333333 1 4 6 14.8
HF896 28.93333333 2 3 6 13.8
HF899 24.13333333 1 0 2 16.3
HF911 28.66666667 0 2 3 13.6
HF909 32.4 4 0 5 18.3
HF915 33.6 0 2 3 14.3
HF932 31.33333333 1 3 5 17.9
HF941 31.86666667 1 1 3 17.9
HF942 39.33333333 1 1 3 15.4
HF943 30.66666667 1 2 4 26.3
HF935 38.66666667 3 1 5 10.6
HF835 27.33333333 0 2 3 15.8
HF326 36.8 1 1 3 13.7
HF339 35.6 2 0 3 20.5
HF347 31.06666667 0 2 3 19.6
HF353 28.8 1 2 4 13.9
HF379 15.86666667 2 0 3 19.6
HF403 36.53333333 2 0 3 14.8
HF404 36.53333333 2 0 3 15.5
HF405 28.93333333 3 0 4 12
HF408 30.66666667 3 0 4 12.3
HF409 20.66666667 1 0 2 19.6
HF410 36.53333333 1 3 5 15.6
HF419 30.4 3 1 5 16.7
HF425 42.4 3 1 5 13.3
HF426 14.66666667 3 1 5 16.6
HF428 33.33333333 2 0 3 18.9
HF438 15.33333333 2 0 3 31.4
HF440 27.86666667 2 1 4 19.4
HF446 32.8 2 1 4 17.4
HF447 31.46666667 1 1 3 13.8
HF456 31.73333333 1 1 3 13.3
HF457 20.53333333 0 2 3 9.2
HF461 17.73333333 2 1 4 15.4
HF477 13.6 2 1 4 16.7
HF478 26.8 1 2 4 12.6
HF482 29.46666667 2 0 3 17
HF489 33.33333333 3 1 5 13.9
HF504 34.8 3 1 5 11.6
HF505 25.86666667 0 1 2 17.7
HF509 36.53333333 1 1 3 19.1
HF511 25.46666667 0 4 5 13.4
HF513 21.6 1 0 2 13.4
HF515 26.26666667 2 0 3 11.6
HF522 18.4 0 4 5 14.3
HF525 33.6 0 1 2 15.6
HF543 28.53333333 2 0 3 18.8
HF547 21.6 2 0 3 17.6
HF549 30.53333333 4 1 6 14.7
HF551 28.93333333 4 1 6 15.7
HF553 44.8 4 1 6 14.6
HF554 27.33333333 0 1 2 19.4
HF556 25.33333333 1 1 3 21.7
HF560 27.46666667 1 2 4 10.4
HF561 29.46666667 0 2 3 16.8
HF568 26.4 3 2 6 16.8
HF572 38 3 2 6 10.3
HF573 22.93333333 3 2 6 23.3
HF574 11.46666667 1 2 4 18.7
HF581 24.8 0 2 3 17.3
HF584 39.46666667 1 3 5 14
HF587 33.46666667 1 3 5 10.8
HF588 23.6 1 2 4 13.6
HF592 19.86666667 1 2 4 14.7
HF593 44.8 4 1 6 16.7
HF597 30.8 4 1 6 16
HF597.5 49.06666667 4 1 6 16
HF599 26.8 4 1 6 19.1
HF600 31.33333333 2 2 5 17.2
HF603 21.2 2 2 5 15.7
HF604 32.66666667 0 2 3 16.9
HF609 34.8 1 1 3 11.6
HF616 21.46666667 2 3 6 19.3
HF634 20.66666667 1 2 4 15.1
HF642 34.8 2 1 4 16.2
HF643 30.8 2 1 4 16.3
HF644 32.53333333 2 1 4 10.4
HF645 31.2 2 4 7 11.4
HF647 24.8 2 4 7 11.8
HF648 41.33333333 2 4 7 14.9
HF649 25.06666667 1 1 3 16.5
HF658 30.13333333 1 1 3 14.6
HF659 29.33333333 0 0 1 19.1
HF670 38.66666667 3 0 4 16.5
HF671 28.26666667 3 0 4 15.1
HF672 16.13333333 0 2 3 12.6
HF675 35.46666667 1 3 5 12.6
HF676 24.8 1 3 5 10.7
HF677 33.86666667 3 2 6 17.9
HF683 31.6 1 4 6 14.9
HF774 32.4 1 4 6 21.1
HF776 24.8 1 2 4 20.3
HF791 32.93333333 1 2 4 17.2
HF792 34.4 3 0 4 16.7
HF796 30.93333333 3 0 4 14.1
HF798 24.93333333 2 0 3 18
HF799 29.33333333 2 0 3 14
HF801 27.6 1 0 2 19.6
HF804 36.53333333 1 0 2 16.9
HF805 30.93333333 1 2 4 16.4
HF808 28.66666667 0 4 5 12.7
HF814 26 1 0 2 16.4
HF816 32.26666667 2 3 6 14.6
HF820 30.66666667 2 0 3 13
HF823 12.4 2 1 4 19
HF825 24.66666667 2 1 4 24.5
HF826 34 2 1 4 18.4
HF827 20.93333333 0 1 2 24.1
HF828 10.26666667 0 2 3