Reference no: EM132213637

Question 1

Senior swimmers participate in competitions for a range of reasons, including fitness, maintaining strength, weight control and as an avenue for social interaction. It is believed that 80% of female senior swimmers rate competition swimming as their main form of fitness training.

(a) State the variable of interest, and suggest an appropriate model to estimate the probabilities of the possible numbers of female senior swimmers in a random group of 15 female senior swimmers who rate competition swimming as their main form of fitness training. 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 a randomly selected group of 15 female senior swimmers, 9 or fewer will rate competition swimming as their main form of fitness training.

(c) Determine the probability that, in a random sample of 55 female senior swimmers, 40 or more will rate competition swimming as their main form of fitness training. State and check any assumptions, conditions or rules of thumb that should be considered before performing the calculations to determine this probability.

Question 2

Performance in the third 100 metres of a 400 metre freestyle swimming race is crucial to the outcome of the race. Based on historical data, the time to complete this third 100 metres amongst senior swimmers in the top 2 divisions has an approximate normal distribution with a mean of 110 seconds and a standard deviation of 17 seconds.

(a) Identify the variable of interest and the unit of measurement of the variable in considering the impact of this part of the 400 metre freestyle swimming race.

(b) Based on historical data, how fast can the top 10% of senior swimmers in the top 2 divisions be expected to complete the third 100 metres of a 400 metre freestyle swimming race this year?

(c) Based on historical data, what proportion of senior swimmers in the top 2 divisions will take more than 135 seconds to complete the third 100 metres of the 400 metre freestyle event?

Question 3

The article, "Health Aging means Happy Aging!" appeared on healthyaging.com on February 29, 2018. Using only the information in this extract below, answer the questions that follow:

It is a widely held belief that exercise and a positive attitude to life enhances wellbeing. But is this true for the "oldies" in our community?
A scientific study has shown that an integrated health education and exercise program (Health Aging and Happy Aging) for community-dwelling older adults was "effective in control of systolic blood pressure and improving self-efficacy for exercise and health-related quality of life".

Researchers from Seoul National University enlisted forty-five hypertensive older adults aged over 65 years who were regular attenders at a Seniors' Centre into their study. Participants were randomly divided into two groups (an intervention and a control group) with the intervention group taking part in a 12 week program of group health education (once a week) and individual counselling (1 time at the 4th week), and patient tailored elastic band exercise (2 times per week).

The study, which appeared in the journal Patient Education and Counseling, was supported by a grant from the Korean Research Foundation. The researchers concluded "Our findings clearly highlight the need for an intervention which focuses on self-management and life style modification with multidisciplinary collaboration."

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

(b) For this study, identify the

(i) response variable(s)
(ii) explanatory variable(s)
(iii) sample size

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

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

Question 4

This question uses information from the data file Swim_18.sav found under the Assessment tab on the StudyDesk (also see Swim_18.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.

In gaining insights into the performance of senior swimmers in the 400 metre freestyle event, a researcher is interested in the ranking of female senior swimmers compared with male senior swimmers. As such she decides to check if there is an association between ‘Gender' and
‘Competition Division' to which a senior swimmer is allocated based on performance in qualifying rounds at competitions approved by the International Masters' Swimming Association.

(a) Use a contingency table to display the relationship between ‘Gender' and
‘Competition Division' for senior swimmers in this study (you should use SPSS to complete this contingency table). The title for this table should reflect the table contents and also include your name. (Note that a table title should appear above a table).

(b) What proportion of female senior swimmers were allocated to Division C?

(c) What proportion of senior swimmers in the study are male and in Division A?

(d) Does there appear to be an association between ‘Gender' and ‘Competition
Division' to which a swimmer is allocated based on qualifying performance? Explain in less than 100 words, using a numerical example(s) from a conditional distribution table to support your explanation. Include the conditional distribution table in your response.

Question 5

Consider the data in the file Swim_18.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 ‘Competition Time' of the male senior swimmers in this study using an appropriate graph produced in SPSS. 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 competition time of male senior swimmers. 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 competition time of male senior swimmers? (Do not copy/paste SPSS output).

(d) What is the median and IQR of the distribution of competition time of male senior swimmers. (Do not copy/paste SPSS output).

(e) For the distribution of competition time of male senior swimmers 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 Swim_18.sav again. To be reassured that qualifying time is a valid measure to use in allocating senior swimmers to divisions, the researcher is interested in identifying if ‘Qualifying Time' can be used to effectively predict how senior swimmers will perform in the International Competition. The researchers decide to investigate this relationship specifically for senior swimmers who have been designated to swim in Division B.

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

(b) Use an appropriate graph to display the relationship between the two variables identified in part (a) for these senior swimmers. 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 these Division B senior swimmers. Justify your choice of this statistic and interpret what it tells you about the relationship.

(e) Use SPSS to find the equation of the regression line which could be used to make predictions and then plot the regression line on the graph in part (b).

(f) Using the regression equation from part (e), predict the expected competition time for a Division B senior swimmer who swam a 520 second qualifying time. Would you expect this to be an accurate prediction? Why or why not?

(g) What proportion of the variability in competition times for Division B senior swimmers can be explained by the model, i.e. the relationship between competition time and qualifying time?