I have a task with Statistics I need help with.

Stat170 - Introductory Statistics

Semester 2, 2015

Assignment 1

Due 5.00pm Wednesday 2nd September via the iLearn link only

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

Instructions:

1) 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.

2) Your assignment should be uploaded as a Word (.doc or .docx) or a PDF file which has been created from a Word processed document ONLY. Other formats, including a PDF created from an image, will not be accepted by the system.

3) Please note that iLearn is fairly reliable, but, like any website, it is occasionally unavailable for short periods. Therefore, do not wait until the due date/time to start trying to submit your work. If you have technical difficulties in submitting your Assignment, it is your responsibility to ensure these difficulties are resolved by the submission deadline. (The University has Help services to support you in the event of a problem; see http://ilearn.mq.edu.au/login/MQ/help.htm.)

Information:

Question 1 (8 marks)

The Adolescent Fitness study was used to investigate factors relating to the health of adolescents living in Australia. 150 subjects, aged from 15 to 19 years took part in the study and the following information was recorded on each subject:

Variable Description

Sex 0 = Male, 1 = Female

Occupation 1 = Full-time student, 2 = In full time employment

3 = Neither studying nor employed full-time

Smoking 0 = Never, 1 = Occasionally, 2 = Every Day

Alcohol 0 = Never, 1 = Usually 1 or 2 alcoholic drinks per week,

2 = Usually more than 2 alcoholic drinks per week

Weight Total body weight (kg)

LeanBodyMass Lean body mass (kg)

MetRate Metabolic rate (number of calories burned in 24 hour period)

a. If possible, list one variable which is:

i. Numerical

ii. Ordinal

1

iii. Nominal

b. The target population for this study was all 15 to 19 year olds living in Australia. Assuming the researchers were not able to select a simple random sample, describe in one or two sentences how you would have selected this sample in order to obtain a representative sample (in regards to the variables recorded in the study) from that target population.

c. Write down the name of an appropriate graph which could be constructed from this study to investigate the relation between Occupation and Metabolic Rate.

d. Write down the name of an appropriate graph which could be constructed from this study to investigate the relation between Occupation and Smoking.

e. Write down the name of an appropriate graph which could be constructed from this study to investigate the relation between Metabolic Rate and Lean Body Mass.

Question 2 (10 marks)

A car manufacturer takes an average of 17.5 hours to construct a car. This includes time for stamping, welding, painting, assembly and inspections. Construction times vary with a standard deviation of 30 minutes and these times follow a normal distribution. Show your working, including an appropriate diagram. (You can simply paste a photo of the diagram into your solution).

a. Find the construction time of a car which is on the 10th percentile of this distribution.

b. What is the probability that a randomly selected car manufactured at this plant takes between 18 and 19 hours to construct?

c. Find the probability that the construction time for a randomly selected car manufactured at this plant is less than 17 hours and 50 minutes.

Question 3 (6 marks)

The Heart Disease study was conducted to investigate risk factors for heart disease in older males. 250 males, all aged over 60 years were selected for the study. Information was recorded on a number of variable, including those described below, for each subject in the study:

Variable Description

Heart Disease Subject has history of heart disease: No, Yes

Alcohol Subject drinks alcohol regularly: No, Yes

The following table was constructed using the information recorded in the Heart Disease study on alcohol consumption and heart disease. Use the table to answer the questions below.

a. What proportion of the males drink alcohol regularly?

b. What proportion of the males with a history of heart disease drink alcohol regularly?

c. Use Minitab to construct an appropriate graphical display to investigate the association between heart disease and alcohol consumption. Ensure your graph has a title and is clearly labelled. You will need to enter the values from the table above (as a 2×2 table) into a Minitab worksheet and select the appropriate options from the Graph menu. Cut and paste your graph into the space below and type in a comment on the association.

Question 4 (16 marks)

Researchers studying the relationship between the size of acorns and the geographic range of the oak tree species recorded information on 28 species of oak from the Atlantic region and 11 from the California region. The data are available in the Minitab file, acorns.mtw, which is in the Assessments folder on iLearn.

Species Latin name of the species

Region 1 = Atlantic 2 = California

Range geographic area covered by the species in km2 x 100

Size typical size of acorn in cm3

Height tree height in metres

Source: Aizen and Patterson. (1990). Journal of Biogeography, volume 17, p. 327-332.

Use the acorns.mtw Minitab worksheet to answer this questions. Follow the instructions below in your answers:

Where a question asks for a percentage, the answer should be expressed as a value between 0% and 100%. Where a question asks for a proportion, the answer should be expressed as a value between 0 and 1.

Give answers to the number of decimal places specified in each part. State units of measurement where appropriate.

a. What was the mean size of the acorns for all species in the study?

(2dp)_______________

b. What was the standard deviation of the size of the acorns from the Atlantic species in the study? (2dp)_______________

c. What was the interquartile range of the tree heights for the Californian species? (integer)_______________

For parts d. to j. you will need to categorise and recode the variable, Range, as follows:

Small: < 2000 km2 x 100

Medium: 2000 km2 x 100 to 10000 km2 x 100

Large: > 10000 km2 x 100

To do this in Minitab, use the Data menu, select Code, select Numeric to Text:

Code data from Columns: select Range

Store coded data in columns: enter a name for the new column, or just overwrite the old column

Original values: enter a data range for each group eg. 0:1999 (for small) etc.

New: enter group names eg. Small etc.

d. What was the median height of trees where the geographic range was medium-sized? (integer)_______________

Question 4 continued

e. How many of the species in the study were found in geographic areas which were small? (integer)____________

f. How many of the Atlantic species were found in geographic areas which were small? (integer)____________

g. What percentage of the species in the study were found in geographic areas which were large? (1dp)_____________

h. What percentage of the Atlantic species in the study were found in geographic areas which were large? (1dp)______________

i. What proportion of the species in the study were both found in the Atlantic and in geographic areas which were small? (4dp)______________

j. Consider the research question: Is the size of an acorn related to the size of the geographic area covered by its species? It has been suggested that the size of a plant’s seed may affect the geographic range of the plant since larger acorns may be carried away by larger animals which may, in turn, have wider territorial ranges. Use Minitab to construct appropriate graphical and numerical summaries to address this research question. Cut and paste your output into the space below and use your summaries to comment on the research question.