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+

The medical expenses for the previous 12 months were recorded and stored in columns 1 to 4, respectively, in C12-03.

Projections for 2016, 2021, 2026, 2031, and 2036 of the numbers of Canadians (in thousands) in each age category are listed here.

a. Determine the 95% confidence interval estimates of the mean medical costs for each of the four age categories.

b. For each year listed, determine 95% confidence interval estimates of the total medical costs for Canadians 45 years old and older.

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Age Category 2016 2021 2026 2031 2035 45-64 10,094 10,054 4,023 2,087 9,892 4,538 2,666 9,823 10,150 4,675 3,669 1,543 65-74 3,375 4,874 3,209 1,193 75-84 1,745 85+ 792 872 973