Question

4.   Birds of many species retain the same breeding partners over many years, yet migration often occurs separately, and male and female overwintering grounds may be separated by thousands of kilometers. If breeding pairs are established, we might expect an association between the day female partners arrive at a breeding ground and the day male partners arrive. Scientists tried to determine if long-term breeding partners exist in a small population of wood thrush (Hylocichla mustelina) in western Pennsylvania. The researchers identified breeding males and females in year 1, and then measured the arrival data of these males and females in year 2 as the number of days elapsed after March 31. Help these researchers determine if there is an association between the arrival date of female and male wood thrush using the small dataset in

4a. What test will you run, and why?

4b. Based on your results, does it appear that this population of wood thrush maintain long-term breeding partners? Why or why not (in other words, give a 1-2 sentence results statement from your correlation).  

4c. Produce a scatterplot with appropriate labels and figure legend.  

Table 4. Arrival date (days after March 31) of female and male wood thrush in a western PA population

Arrival Date of Female (days)	Arrival Date of Male (days)
21	3
23	3
37	4
19	6
24	6
33	8

Answer 1

• Here, we would like to determine if there is a correlation between the couples.
  Hence, a test for correlation would be appropiate here.
  We are to test:
  
  
  We use the test statistic:
  
  where,
  
  
  We reject H0 at 5% level of significance iff
  
  where,
  
  
  
  
  
• 
  
  hence, we observe that,
  
  
  Hence, we fail to reject the Null Hypothesis at 5% level of significance, and hence, we conclude that, the correlation among the birds do not maintain long term breeding partners.
  
  
• For the scatterplot, we use the following code in R
  
  > x=c(21,23,37,19,24,33)
  > y=c(3,3,4,6,6,8)
  > plot(x,y,ylab="Arrival Date of Male Birds",xlab="Arrival Date of Female Birds", main="Scatterplot")
  
  We get the following plot as output:
  
  
  In Excel, the data is put in like this and the following option is selected, as shown in the screenshot.
  
  
  We get the following Graph generated.
  
  
  

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