Tasmanian devils are endangered due to a contagious facial tumour disease that threatens the survival of the species. A recent survey in the Cradle Mountain region of Tasmania located 136 Tasmanian Devils.  Forty-nine of these animals were not diseased and eighty-seven had contracted the disease. Questions 1 and 2 are based on these data.  Information relating to each of the Tasmanian devils was recorded as follows:

Sex  sex of Tasmanian Devil:  1 = male,  2 = female

Age  age of Tasmanian Devil:  1 = young,  2 = adult,  3 = elderly

Diseased  whether Devil was diseased or not:  0 = diseased,  1 = not diseased

Length  total length from tip of nose to tip of tail in cm

Weight  weight in kg

Headlength  length of head in cm

Height   height at shoulder in cm

Skull  width of skull in cm

Marking  location of white body markings:

1 = chest only, 2 = chest & rump, 3=none

Question 1  

a)  Define a target population for the data outlined above.

b)  If you wished to compare the general health of Devils with the tumours to the general health of Devils without the disease but you only had the resources for a vet to examine 20 of the Tasmanian Devils in this study, give a detailed explanation of how you would decide which 20 animals to examine. 

c)  Write down all the categorical variables and indicate whether they are nominal or ordinal.

d)  Indicate a graphical display which could be constructed from the variables described above to:

  i.  determine whether skull size is dependent on a Tasmanian Devil’s length

  ii.  compare weights of male and female Tasmanian Devils

  iii.  determine whether body markings are associated with whether or not a Tasmanian Devil contracts the disease

The weights of mature male Tasmanian Devils are normally distributed with a mean of 11kg and standard deviation of 0.8kg. Use this information to answer the following questions. You must show your working for these questions. You can type the formulae for your answers on one line, for example: z=(y-m)/s or z=(y-bar-m)/(s/Ön), or, if you are a more confident Word user you can use the equation editor in Word to form your equations. Alternatively, you can include your (neat!) hand-written equations (and diagrams if you wish) by photographing them so that you have the images saved as picture files and then pasting these into your solution.

a)  A conservationist conducting a study of Tasmanian Devils wants to determine the effects of weight on overall health.  He intends to sample mature male Tasmanian Devils which weigh at least 10.5kg.  If 100 mature male Tasmanian Devils are selected at random, how many are expected to meet the requirement for his study?

b)  A special breeding programme has been designed for mature male Tasmanian Devils. Only those with weights among the heaviest 3% are to be included in the programme.  What is the lightest weight a mature male Tasmanian Devil can have to be eligible for this breeding programme?

c)  The ideal body weight for a mature, adult male Tasmanian Devil is between 10.2 kg and 12 kg. Find the percentage of mature adult male Tasmanian Devils which are in the ideal weight range.