Virtually all countries have universal government-run health care systems. The United States is one notable exception. This is an issue in every election, with some politicians pushing for the United States to adopt a program similar to Canada's. In Canada, hospitals are financed and administered by provincial governments. Physicians are paid by the government for each patient service. As a result, Canadians pay nothing for these services. The revenues that support the system are derived through income taxes, corporate taxes, and sales taxes. Despite higher taxes in Canada than those in the United States, the system is chronically underfunded, resulting in long waiting times for, sometimes, critical procedures. For example, in some provinces, newly diagnosed cancer victims must wait several weeks before treatments can begin. Virtually everyone agrees that more money is needed. No one can agree however, on how much is needed. Unfortunately, the problem is going to worsen. Canada, like the United States, has an aging population because of the large numbers of so-called baby boomers (those born between 1946 and 1966), and because medical costs are generally higher for older people. One of the first steps in addressing the problem is to forecast medical costs, particularly for the 20-year period starting when the first baby boomers reached age 60 (in 2006). A statistics practitioner has been given the task of making these predictions. Accordingly, random samples of four groups of Canadians were drawn.

They are Group Ages

1 45-64

2 65-74

3 75-84

4 85+

In the attached Excel sheet, the medical expenses for the previous 12 months were recorded and stored in columns A to D, respectively (Source: Statistics Canada).

(a) Suppose you are the decision maker and have a claim to investigate about the population of the above problem. Clearly explain your statistical hypothesis and develop appropriate null and alternative hypotheses. What would be your conclusion? Show your work.

(b) Do these data provide sufficient evidence at 2% significance level that the mean medical cost for age group 3 is greater than the mean medical cost of age group 1? Show your work. (2mark)

(c) Do these data allow us to infer that there are differences in the medical cost between the four age groups. Show your work. (2 Marks)

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