## Evaluate the statistical arguments, Advanced Statistics

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Evaluate the following statistical arguments. Begin by identifying the sample, population, and the property which is being investigated. Do these arguments sound acceptable? Would more information be required?

(i) From the NRL's annual report, we learn that all of the sixteen ongoing clubs selected for spot audits last year had financial irregularities sufficient to qualify the auditor's report.

Wherever they shone the light - and they shone it in four clubs - they found trouble. Not one decent effort. Clearly the league clubs just aren't complying with their affiliation requirements concerning financial probity.

(ii) Research has shown that Australians feel strongly about the importance of increasing funding for essential services such as hospitals, schools, and banks in rural areas. A telephone survey of 2,000 households was conducted, to gauge people's opinions about the importance of ensuring better funding for rural communities. To ensure that the interests of both urban and rural communities were represented, half of those surveyed were in rural areas, and half in urban areas. It was found that over 70% of those surveyed believed that providing adequate funding for these services was very important. In an election year, this is something the Government should be thinking about very closely. The views of 70% of Australians cannot be ignored.

(iii) A newspaper report] Computer theft is not a great problem in Australian offices, according to a recent survey. Only 39% of middle managers questioned agreed that computer theft would be the most likely cause of future unplanned expenditure on information technology. By contrast, 57% of managers in New Zealand, 41% of managers in the United Kingdom, and 55% of managers in Canada agreed with the question.

(iv) In 1872 Francis Galton conducted a study into the efficacy of prayer. The main argument of his study was as follows.

Many thousands of prayers are offered each day for the long life and good health of the monarch and the royal family, whether they be prayers in church, bedside prayers of children, or even the prayer contained in the national anthem. Moreover, praying for the health of the royal family is a longstanding tradition in the United Kingdom. If prayers can be efficacious, then surely at least some of these prayers will have been efficacious, and so one would expect to find the lives of members of the royal family longer than the lives of other people.

So Galton collected data from the death notices of leading newspapers on the average age at death of men who had reached the age of thirty, and whose deaths fell between 1758 and 1843 (deaths by accident and violence excluded). Members of the royal family (97 men) had an average age at death of 64.04, compared to 69.49 for clergymen (945 men sampled), 68.14 for lawyers (294 sampled), 67.31 for doctors and surgeons (244 sampled), 67.31 for aristocrats (1179 sampled), 70.22 for gentry (1632 sampled), 68.74 for merchants (513 sampled), 68.40 for naval officers (366 sampled), and 67.07 for army officers (569 sampled). Hence Galton concluded that members of the royal family did not tend to live longer than other people, and so that prayer is not efficacious.

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