This assignment will provide you the opportunity to further develop your skills in linear regression, Chi-square analysis, and non-parametric analysis. Through this assignment, you will evidence all four of the unit learning outcomes.
There are three questions in this assignment. You will perform statistical analyses on all three questions. Statistical analyses will include selecting the most appropriate analysis method / hypothesis test, performing descriptive statistics (where relevant), stating and checking assumptions, performing appropriate estimations (where relevant), and performing hypothesis testing. You are expected to present your analyses in a scientific manner. This means that figures and tables should be formatted appropriately (with captions/titles and axis labels) and written text should guide your reader through your analyses, justifications, and interpretations.
Google reports that 42% of eligible Australians have not received their COVID-19 vaccine, 21.5% have received 1 dose of vaccine, and 36.5% are fully vaccinated having received 2 vaccine doses. These proportions were investigated by randomly sampling 200 individuals. Use the data in the ‘Q1_Vaccine’ sheet to determine whether there is evidence that the vaccination proportions are aligned to those reported by Google (use = 0.01).
Vitamin D is known as the sunshine vitamin. It is naturally produced in skin cells upon exposure to UV light. Using sunscreen can inhibit this process by reducing the amount of UV light that skin is exposed to. Thus, it is thought that people who are diligent in using sunscreen may be at increased risk of becoming Vitamin D deficient. One way to overcome this is to consume Vitamin D in the diet. To determine whether blood Vitamin D levels could be predicted from the amount of sun exposure (hours/week), using sunscreen (or not), and the amount of Vitamin D consumed in a standard diet (international units, IU), a group of researchers recruited 50 participants.
- Use the data in the ‘Q2_VitaminD’sheet and α = 0.05 to determine whether blood Vitamin D levels can be predicted from the above-mentioned variables. Which, if any, of the predictors listed contribute significantly to predicting blood Vitamin D levels?
- Write the model equation and use it to predict the blood Vitamin D level from the following: sun exposure = 18 hours/week, sunscreen use = yes, and dietary Vitamin D = 32 IU. Include confidence interval estimations for the mean Vitamin D level expected and the prediction interval estimation for an individual prediction.
Public education campaigns are thought to increase participation in new programs. A state government developed a public education campaign in attempt to reduce the amount of household waste generated each year. To assess the campaign’s effectiveness, the government ran it for a year in randomly selected councils. They then weighed the household waste from 24 households in councils that ran the campaign and 24 households in councils that did not have the campaign. The corresponding data can be found in the ‘Q3_Waste’ sheet. Using an α = 0.05, do the data suggest that waste is reduced in households in councils where the campaign ran?