Stat170 - Introductory Statistics Semester 1, 2014

Assignment 1

Due 9th April 5.00pm via the iLearn link only

Submit via the Assignment 1 link in the ASSESSMENTS area of iLearn.

Instructions: • The answers to all questions are to be word processed. You can either type formulae into your solution or you can use the equation editor in Word or you may include hand-written equations and diagrams by photographing them so that you have the image saved as a picture file and then pasting (inserting) the image/s into your solution.

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• This Assignment is worth 6% of your total grade for STAT170. You may discuss the Assignment with your classmates if you wish, but must then complete all of the calculations and writing by yourself. Note: every semester, several students receive a mark of 0 for this Assignment, due to plagiarism. Ensure that you do not copy parts of your friends' Assignment submissions. Submitting your assignment via iLearn is a declaration that the work is your own.

Information:This assignment is worth 6% and is marked out of 35. Penalties apply as follows:

Submitted on Wednesday after 5pm: Deduct 5 marksSubmitted on Thursday: Deduct 10 marks Submitted on Friday: Deduct 20 marks

No assignments submitted after Friday will be accepted.

Q1 Q2 Q3 Q4 Total9 marks 10 marks 6 marks 10 marks 35 marks

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 = femaleAge age of Tasmanian Devil: 1 = young, 2 = adult, 3 = elderlyDiseased whether Devil was diseased or not: 0 = diseased, 1 = not diseasedLength total length from tip of nose to tip of tail in cmWeight weight in kgHeadlength length of head in cmHeight height at shoulder in cmSkull width of skull in cmMarking location of white body markings:

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

Question 1 (9 marks)

• Define a target population for the data outlined above.

A: Tasmanian Devils living in the cradle mountain region of Tasmania of varying degrees of size and health

• 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.

A: Using collected data, I would determine the ratio of Tasmanian devils with & without facial tumours, as well as Male/female. I would then determine the numbers of each group in relation to a sample size of 20. This would allow me to collect the correct number of bot variable groups to be used in a sample size of 20.

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

Sex: Nominal Markings: Nominal Diseased: Nominal

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

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

Q: A scatter Plot would be appropriate with Length as the X axis and Skull size as the Y variable.

• compare weights of male and female Tasmanian Devils

Q: The appropriate graph is a histogram for these variables.

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

Q:A Clustered bar chart would be the best graphical displayed to be used in this variable comparison.

Question 2 (10 marks)

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-µ)/σ or z=(y-bar-µ)/(σ/√n), 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 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?

A: z=(y-µ)/σ y=10.5 µ=11 σ=0.8 z=(10.5-11)/0.8

: z=-0.625 is .2875 meaning that it is 1-z=.7125Therefore: 71 of the Tasmanian devils will meet the requirements needed.

• 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?

A:The answer is 13.17kg. z=97%=.03 y=? u=11 σ=.8

• 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.

A: The ideal weight range is of a percentage of 71.4%

The 2012OLYMPICS.MTW Minitab worksheet, available in the Assessments area of iLearn, contains information on the 85 countries which won medals at the 2012 Olympics in London.

The variables recorded in the 2012OLYMPICS.mtw worksheet are:

Variable Name Variable Description

Country Name of country

Region Location of country:

1 = Africa 2 = Americas 3 = ANZ (Australia and New Zealand)

4 = Asia 5 = Europe

Rank Final ranking in medal tally

Gold Number of gold medals won

Silver Number of silver medals won

Bronze Number of bronze medals won

Total Total number of medals won

Question 3 (6 marks)

From the 2012OLYMPICS.MTW worksheet use Minitab to obtain the following information.

• Which region had the greatest number of participating countries? 5

•

• What was the total number of medals won by Australia and New Zealand (ANZ)?

48

• What proportion of the medals won by Australia and New Zealand (ANZ) were gold?

13/48 = .271

• What percentage of all medals won by African countries were gold?

15 of 46 equals 32.61%

• How many of the European countries won silver or bronze medals but no gold?

11 won bronze or silver but no gold

• Of the total number of medals won by the Americas, what proportion were won by the

United States? 104 of 184 equals 0.565_____

• How many of the medals won were gold medals? 302

_________________________________

• What proportion of the gold medals were won by China? 38 of 302 = .126

• Of the countries ranked 79th on the medal tally, what percentage were African

countries? 1 out of 7 therefore 14.29 percen

• Which region won a higher proportion of the gold medals, Asia or Europe? Europe

Question 4 (10 marks)

Use the 2012OLYMPICS.mtw worksheet and Minitab to produce an appropriate graphical display and an appropriate summary table to address the research question above. Your output should only contain information about Total medals (C7) for European and Asian

countries. All output must have clear labels and titles.

Use the space below to create a short report containing your graph and summary table, together with appropriate comments addressing the research question. Only include relevant output from Minitab. Make sure your output has appropriate labels. As for the rest of this assignment, comments must be word-processed with the output cut-and-pasted from Minitab. The computer output and comments should not exceed this page.