Question 1

Use this extract taken from the article, "Physical activity reduces immobility in older adults" (from Aged Health, September 2017) to answer the questions that follow:

In the light of recent concerns about the aging population and its impact on government policy, a study conducted by researchers at Mount Olivet University concluded that doing even a small amount of moderate exercise per week can lead to an improvement in overall physical functioning in older adults.

In the study, the researchers evaluated how different amounts of exercise for adults aged 65-89 improved the mobility of participants. While the researchers saw improvements in all subjects who added some physical activity to their routine, those who got more exercise saw greater changes.

Over a period of 3 years, researchers analysed data from 540 men and 430 women aged 65-89. Half were randomly assigned to a program of walking and light physical training; the other half participated in health education workshops. At the start of the study, all had low levels of physical functioning and reported fewer than 20 minutes per week of regular physical activity in the month prior to starting. Participants were evaluated as the study commenced, and then again every six months. The researchers relied on self-reporting to measure physical activity outside study sessions.

After 3 years, it was found that changes in activity were significantly greater in the physical activity intervention group than the group who solely participated in health education workshops. It was also noted that a greater amount of physical activity corresponded to a larger improvement in mobility.

"People just want to live healthy, independent lives and this group are at risk of losing that. Maintaining functional independence for older adults is an important public health issue, and impacts government policy in terms of infrastructure and support services. In earlier studies, we confirmed that regular exercise can help improve physical function and prevent mobility loss. Now we see that even a small increase can have a big impact," said researchers.

(a) Is this particular study that was cited in the article observational or experimental? In less than 50 words clearly explain your choice based on the extract given above.

(b) Identify the

(i) variable(s) of interest
(ii) explanatory variable(s)
(iii) sample size

(c) Are the four principles of experimental design used in this study? Explain your answer in context.

(d) Identify and discuss one possible limitation with this study.

Question 2

According to data recently released by the Australian Bureau of Statistics, the most commonly reported main field of study for people aged 15 to 64 years enrolled in a tertiary institution is management and commerce, with 25% of those enrolled choosing this field of study.

A random sample of 10 people between the ages of 15 and 64 years were selected from the Springfield campus and surveyed to determine their field of study. The variable of interest is the number of people between the ages of 15 and 64 years who are studying management and commerce.

Use this information to answer the following questions:

(a) Suggest an appropriate model to estimate the probabilities of the number of people between the ages of 15 and 64 years who are studying management and commerce.

i. Name the appropriate model.
ii. What are the parameters of this model for this context?
iii. Explain why this model is appropriate by discussing the important distinguishing features of the model.

(b) Using the model from part (a), estimate the probability that, in the randomly selected sample of 10 people from the Springfield campus aged 15 to 64 years, 5 or more will be studying management and commerce.

(c) A random sample of 110 people aged between 15 and 64 years have been selected from the Toowoomba campus to determine their field of study. For this sample of 110, calculate the mean and standard deviation of the number of people aged 15 to 64 years who are studying management and commerce.

(d) Determine the probability that, in the random sample of 110 people (selected in part (c)), 20 or more will be studying management and commerce.

(e) State and check any assumptions, conditions or rules of thumb that should be considered before performing the calculations to determine the probability in part (d).

Question 3

This question uses information from the data file koalas17.sav found under the Assessment tab on the StudyDesk (also see koalas17.txt for more details about the study and the variables measured). Make sure the variable view in SPSS is setup correctly with all ‘labels' correctly defined (with units), all ‘values' assigned correctly for categorical variables and the correct ‘measure' selected for all variables.

As a researcher seeking to gain insights into the variables measured in this study, you are interested in ascertaining if there is a relationship between gender and age (either adult or juvenile) of koalas in South East Queensland.

(a) Using SPSS, produce a contingency table to display the relationship between Gender and Age for koalas in this study. The title for this table should reflect the table contents and also include your name. (Note that a table title should appear above the table). You can copy and paste this table straight into your assignment; just ensure you have a meaningful title.

(b) With reference to this study, what proportion of koalas are female?

(c) With reference to this study, what proportion of adult koalas are male?

(d) Based on the data from this study, does there appear to be an association between Gender and Age in the population of koalas living in South East Queensland? Explain in less than 100 words, using a numerical example(s) from a conditional distribution table to support your explanation.

Question 4

Police response time to an emergency is defined as the difference between the time an emergency call is first received and the time a police car radios that it has arrived at the scene. Over a long period of time, it has been determined that police response times have a normal distribution with a mean of 8.2 minutes and a standard deviation of 1.7 minutes.

(a) Identify the variable of interest and the unit of measurement of the variable.

(b) What proportion of response times will take less than 5 minutes?

(c) What proportion of response times will take between 6 and 9 minutes?

(d) Public relations officers want to reassure the public about the response times of the police to emergencies, and are issuing a statement to the media. What time should they quote in their press release such that no more than 5% of response times will take longer than this time?

Question 5

Consider the data in the file koalas17.sav again. Use SPSS to find the answers to the following questions, but do not copy and paste SPSS output into your answer for parts (c) and (d) (make sure you always include units where appropriate).

(a) Display the distribution of Crown Density of the trees measured in this study, using an appropriate graph. Label the axes correctly, include units of measure and provide an appropriate title. Include your name in the title of your graph.

(b) Using the graph in (a) only (don't refer to SPSS summary statistics), describe in no more than 60 words, the distribution of Crown Density. Include comments on shape, centre and spread of the distribution and the existence of outliers, if any. Do not include information from any calculations, use the graph only.

(c) What is the sample size, mean and standard deviation of the distribution of Crown Density of trees in the study? (Use SPSS, but do not just copy/paste SPSS output).

(d) Using SPSS find the median, first quartile, third quartile, and IQR of the distribution of Crown Density of trees in the study? (Do not copy/paste SPSS output).

(e) For the distribution of Crown Density in part (a), which statistics are appropriate to measure the centre and spread? Give a reasonable explanation for your choice.

Question 6

Consider the data in the file koalas17.sav again. As a researcher you are interested in seeing if Height of Tree can be used effectively to predict Crown Size of Tree, especially since research suggests that crown size has an impact on the size of koala populations.

(a) What are the two variables you will need to include in your analysis? What type of variables are they? What are the units of measure of these variables?

(b) Use an appropriate graph to display the relationship between the two variables identified in part (a) for the trees in this study. Label the axes correctly, include units of measure and provide an appropriate title. Include your name in the title of your graph.

(c) From the graph in part (b), describe (in no more than 30 words) the form, direction and scatter of this relationship, and identify any outliers.

(d) Calculate an appropriate statistic to measure the strength and direction of the relationship between the two variables for the trees in this study. What proportion of the variability of crown size is accounted for by the linear regression on height of trees?

(e) Use SPSS to find the equation of the regression line which could be used to predict the crown size of a tree from the height of the tree:

i. State the regression equation,
ii. Plot the regression line on the graph in part (b),
iii. Interpret the slope of the regression line,
iv. Interpret the intercept of the regression line.

(f) Based on the data in this study, do you think that using a linear regression model is appropriate for predicting crown size from height of a tree? Give two reasons to support your decision.