QuestionQuestion

Section 1

1. You have collected data on how much each of 100 randomly selected Hollywood films and 100 randomly selected Bollywood films cost to make, and how much each one grossed at the box office. You want to know if films that cost more to make also make more money, and if the trend is different for Hollywood and Bollywood movies. What test would you use? Why?

2. You are studying the soil characteristics in three forest patches: one dominated by beech, one dominated by oak, and one dominated by conifers. You randomly select 10 points in each patch and measure the soil pH at each one. You want to know whether soil pH differs among the forest patches. What test would you use? Why?

3. Chimpanzees exhibit many forms of tool use, including termite fishing, nut hammering, and resin pounding. You observe 20 individual chimpanzees from each of three troops, and record which of these three behaviours each individual uses most often. (That is, you record only the most common behaviour for each individual.) You want to know whether preferred behaviours differ among troops. What test would you use? Why?

4. You are doing a study on extra sensory perception (ESP). You want to know if people are better at guessing when the reward they can gain for being correct is larger. You set up an experiment in which participants must choose between two identical boxes, one on the right and one on the left. In one of the boxes, you hide some amount of money between £1 and £10. The other box is empty. If the participant chooses the box with the money, they get the money. If they choose the empty box, they get nothing. You do this test 100 times, once with each of 100 different participants, and different amounts of money each time. You want to find out if the probability that participants are correct depends on the reward. What test would you use? Why?

5. You are studying two species of ladybird beetles, and you want to know which one is the more efficient predator. You conduct an experiment in which you place a beetle on a leaf with 3 aphids, and you record how many aphids the beetle eats in 2 minutes. You do this for 10 beetles from each species. What test would you use to compare the predation efficiencies of the two species? Why?

Section 2.1

You are training a sled dog team. There are three food types you can feed your dogs: fish (i.e., fish-based), mixed (i.e., mixed meat and fish), and grain (i.e., grain-based). You want to know which food maximises performance. You enlist a friend who also trains sled dogs to help you do an experiment. You randomly select dogs from your teams to get each food type. After the dogs have been on the experimental diets for two weeks, you test each dog’s performance in a 10 km solo run with a training sled. You record each dog’s time for the test run. You assign 10 dogs from your team to each food type. Your friend assigns 10 dogs to the fish diet, 10 dogs to the mixed diet, and 5 dogs to the grain diet. You analyse the data with the tests below.

1. What test have you used? (2 marks)
2. Report your results in a clear and concise format. (No figure is needed. 15 marks)
3. Across all trials, your friend’s dogs ran faster than yours. He argues that this is evidence that his team is better, and you missed it because you did not do a Tukey test that includes teams. Is his argument correct? Why or why not. (3 marks)

> sd.aov=aov(time~food.type+team+food.type*team,data=sleddogs)
> summary(sd.aov)

               Df Sum Sq Mean Sq F value Pr(>F)
food.type       2 113.0   56.50   3.541 0.0366 *
team            1   18.7   18.75   1.175 0.2837
food.type:team 2   21.5   10.77   0.675 0.5139
Residuals      49 781.8   15.96               
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> sd.aov=aov(time~food.type+team,data=sleddogs)
> summary(sd.aov)

            Df Sum Sq Mean Sq F value Pr(>F)
food.type    2 113.0   56.50   3.587 0.0349 *
team         1   18.7   18.75   1.190 0.2804
Residuals   51 803.3   15.75               
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> sd.aov=aov(time~food.type,data=sleddogs)
> summary(sd.aov)

            Df Sum Sq Mean Sq F value Pr(>F)
food.type    2 113.0   56.50   3.574 0.0351 *
Residuals   52 822.1   15.81               
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


> TukeyHSD(sd.aov)

Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = time ~ food.type, data = sleddogs)

$food.type
                diff       lwr       upr    p adj
grain-fish   1.196923 -2.079630 4.4734760 0.6543957
mixed-fish -2.300310 -5.333808 0.7331886 0.1700899
mixed-grain -3.497233 -6.773786 -0.2206801 0.0339464

> mean(sleddogs$time[which(sleddogs$team=="your.team")])
[1] 32.01056

> mean(sleddogs$time[which(sleddogs$team=="friends.team")])
[1] 30.53815

Section 2.2

In many animal species, offspring prefer mates that look like their opposite-sex parents. That is, females prefer males that look like their fathers, and males prefer females that look like their mothers. Bressan (2020, Scientific Reports) studied mate choice by eye colour in human females in Italy. She surveyed 780 women between the ages of 19 and 54. For each woman, she recorded i) the colour of the woman’s eyes, ii) the colour of the woman’s mother’s eyes, iii) the colour of the woman’s father’s eyes, and iv) the colour of the woman’s partner’s eyes (if the woman had a partner). She classified eye colours as simply “blue/green” or “brown.” She also conducted a test in which she asked women to look at two photographs of the same male face. In one photograph the eye colour had been manipulated to be blue, and in the other it had been manipulated to be brown. She asked each woman to choose which face she would prefer for a long-term partner.

For the practice test, you asked whether a woman’s own eye colour and the eye colours of her parents predict the eye colour of her partner. Here, you will ask whether a woman’s own eye colour and the eye colours of her parents predict the eye colour she would prefer in a partner. (These are different questions, because people do not always choose partners that match their reported preferences.) You have conducted logistic regressions, where the response variable is whether the woman chose the photograph with blue eyes (1 for yes, and 0 for no). The predictors are her eye colour (OWN_bluegreen), her father’s eye colour (FATHER_bluegreen), and her mother’s eye colour (MOTHER_bluegreen). Using the outputs provided, answer the following questions:

(The data set is in the Dropbox folder with the other data for this test, but you do not need to reanalyse the data. The outputs below are sufficient to answer the questions.)

1. Report the results of your analysis for all three predictors in a clear and concise format.
2. If a blue-eyed woman’s father had blue eyes, what is the probability that she chose the blue-eyed photo? If a brown-eyed woman’s father had brown eyes, what is the probability that she chose the blue-eyed photo?
3. A colleague observes that women with blue-eyed fathers are more likely to have blue eyes themselves. Therefore, he argues, we cannot determine whether the woman’s father’s eye colour influences her preference. Perhaps the women simply preferred photographs with eye colours that matched their own eyes, and the apparent relationship between the women’s preferences and the fathers’ eye colour is an artefact of this other relationship. Is your colleague’s argument plausible? Why or why not?

> cbg=glm(CHOSE_bluegreen~OWN_bluegreen+MOTHER_bluegreen+FATHER_bluegreen,data=bdss)
> summary(cbg)

Call:
glm(formula = CHOSE_bluegreen ~ OWN_bluegreen + MOTHER_bluegreen +
    FATHER_bluegreen, data = bdss)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-0.6116 -0.5034   0.3885   0.4812   0.5894

Coefficients:
                Estimate Std. Error t value Pr(>|t|)   
(Intercept)       0.42972    0.02949 14.572 < 2e-16 ***
OWN_bluegreen    0.10819    0.04112   2.631 0.00867 **
MOTHER_bluegreen -0.01906    0.03879 -0.491 0.62328   
FATHER_bluegreen 0.07364    0.03908   1.884 0.05992 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.2458424)

    Null deviance: 194.49 on 777 degrees of freedom
Residual deviance: 190.28 on 774 degrees of freedom
(2 observations deleted due to missingness)
AIC: 1122.3

Number of Fisher Scoring iterations: 2

> cbg=glm(CHOSE_bluegreen~OWN_bluegreen+FATHER_bluegreen,data=bdss)
> summary(cbg)

Call:
glm(formula = CHOSE_bluegreen ~ OWN_bluegreen + FATHER_bluegreen,
    data = bdss)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-0.6014 -0.5008   0.3986   0.4762   0.5768

Coefficients:
                Estimate Std. Error t value Pr(>|t|)   
(Intercept)       0.42315    0.02628 16.103 < 2e-16 ***
OWN_bluegreen    0.10063    0.03811   2.640 0.00845 **
FATHER_bluegreen 0.07761    0.03822   2.031 0.04263 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.2456018)

    Null deviance: 194.49 on 777 degrees of freedom
Residual deviance: 190.34 on 775 degrees of freedom
(2 observations deleted due to missingness)
AIC: 1120.5

Number of Fisher Scoring iterations: 2

Section 3.1

Flight metabolic rate is often used as a measure of flight performance in insects. Lebeau and colleagues (2016, Proceedings B) studied flight metabolic rate in the meadow brown butterfly Maniola jurtina. They collected 87 female butterflies from two different agricultural habitats, one intensively managed and extensively managed. They recorded the mass of each butterfly (in mg) and the site from which it was collected (in the column origin of their data set, i for intensively managed, e for extensively managed). They recorded the resting metabolic rate (RMR) for each butterfly (in ml CO2 hr-1). They measured the flight metabolic rate (FMR) for each butterfly on a flight mill. Butterflies are ectotherms, so their metabolic rates may depend on the ambient temperature. Therefore, they recorded the temperature (in C) at the time of each flight test. Their data can be found in the spreadsheet “butterflies.csv”

Does the flight metabolic rate of meadow brown butterflies depend on their resting metabolic rate, their mass, the ambient temperature, and/or interaction between butterfly mass and ambient temperature? Present your code, and report your results clearly and concisely. Provide a figure to support your results.

Section 3.2

Using the same data set as above, is the mean mass of meadow brown butterflies different in the intensively managed and extensively managed sites? Present your code, and report your result clearly and concisely. Support your result with a figure. (15 marks)

Section 3.3

The golden mantella (Mantella aurantiaca) is a tropical frog native to Madagascar. The species is endangered in the wild, and is now conserved mostly in captivity. The golden mantella call can consist of a single pulse (e.g., here), a double pulse (you can hear a few in this video), or rarely a triple pulse. Conservationists are concerned that the frog’s calls may be changing in captivity, and that these changes may mean the frogs will be less able to survive if they are released into the wild in the future. You record 100 golden mantellas in the captive population at Chester Zoo and 44 in the wild in Madagascar, and you note which call type each individual uses most often. In the Chester Zoo population, 74 frogs used the single call most often, 20 used the double call most often, and 6 used the triple call most often. In the wild population, 24 frogs used the single call most often, 14 used the double call most often, and 6 used the triple call most often. Does this data provide evidence that frogs use calls differently in the captive and wild populations? Present your code, and report your result clearly and concisely.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

Section 1

1. You have collected data on how much each of 100 randomly selected Hollywood films and 100 randomly selected Bollywood films cost to make, and how much each one grossed at the box office. You want to know if films that cost more to make also make more money, and if the trend is different for Hollywood and Bollywood movies. What test would you use? Why?

Answer: A rank correlation test to test the strength of association between between cost and revenue movies take, first on combined films ie. including both hollywood and bollywood, then test the association within each group would be appropriate in this case. Predictor and response variables both are quantitative.

2. You are studying the soil characteristics in three forest patches: one dominated by beech, one dominated by oak, and one dominated by conifers. You randomly select 10 points in each patch and measure the soil pH at each one. You want to know whether soil pH differs among the forest patches. What test would you use? Why?

Answer:

Anova test is preferable as it would be helpful to test if there is any difference in soil pH values among three groups. Two-way anova would be used as a predictor is a categorical variable with three independent groups: beech, oak and conifers and response variable is the quantitative i.e. soil pH value.

3. Chimpanzees exhibit many forms of tool use, including termite fishing, nut hammering, and resin pounding. You observe 20 individual chimpanzees from each of three troops, and record which of these three behaviours each individual uses most often. (That is, you record only the most common behaviour for each individual.) You want to know whether preferred behaviours differ among troops. What test would you use? Why?

Answer: Fisher’s exact test can be used (as sample size is less, otherwise chis-square would be used) to test if observed frequencies ie. The frequency of chimpanzees falling in each group from the 20 samples is consistent with the expected frequency or not (expected frequency would be equal frequency in each group)....

By purchasing this solution you'll be able to access the following files:
Solution.docx.

$65.00
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

Find A Tutor

View available Statistics-R Programming Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

Decision:
Upload a file
Continue without uploading

SUBMIT YOUR HOMEWORK
We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

  • 1
  • 2
  • 3
Live Chats