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STA2300 Data Analysis

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Questions

1. According to the Australian Bureau of Statistics, 70% of all Australian men aged 18 and over are overweight or obese. A former STA2300 student takes a random sample of 20 men aged 18 years and over in Toowoomba. A particular variable of interest is the ‘number of men aged 18 and over who are overweight or obese’. Based on the above information answer the following questions:

(a) What is an appropriate model to represent the variable of interest? Write down the parameters of the model, if any.

(b) Discuss how the conditions of the appropriate model are satisfied in the current study.

(c) Find the mean and standard deviation of the number of men aged 18 years and over who are overweight or obese using the parameters of the model.

(d) Find the probability that at least 15 of the men aged 18 years and over are overweight or obese.

(e) Determine the probability that, in a random sample of 100 men aged 18 years or more in Toowoomba, 75 or more men are overweight or obese. State and check any assumptions, conditions or rules of thumb that should be considered before performing the calculations to determine this probability.

2. Use this extract taken from the article, “Combination of Garlic and Lemon juice prevent blood sugar of diabetic patients,” (appeared in Diabetes Research on October 31, 2016) to answer the questions that follow:

Diabetes is considered as one of the major public health problems worldwide. It is a chronic disorder in which a person has high blood sugar because the body does not produce enough insulin. Diabetes is the major cause of mortality and morbidity in the world. A recent study by researchers at the US Diabetes Research Centre and Oklahoma University School of Public Health investigated the effects of a mixture of garlic and lemon juice on diabetic patients in the US.

A double-blinded, randomized, placebo-controlled trial was conducted with 360 diabetic patients. Randomization was stratified by gender. Patients were randomly assigned to one of four groups. Each group consisted of 45 men and 45 women. The first group was assigned to receive the mixture of garlic and lemon juice daily, the second group was given 20 grams fresh garlic daily, the third group was given 1 tablespoon lemon juice daily, and the last group was not given any intervention. After fifteen weeks of intervention, it was found that the HbA1C (three-month average sugar level) of the combined garlic and lemon juice group was significantly lower compared with the other groups.

The researchers also found a greater reduction in BMI, systolic and diastolic blood pressure in the mixed group compared with garlic, lemon juice and control groups.

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

(b)  For the above study identify, if appropriate, the

i) response variable(s).
ii) factor and its levels.
iii) sample size.

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

(d) Explain explicitly what a confounding variable is. Identify one plausible confounding variable in this study and explain why it is a confounding variable.

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