Regression analysis and experimental design, Applied Statistics

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For many decades, there has been considerable attention paid to identifying various factors that help to reduce the number of fatalities on Australian roads. In 1964 Victoria and South Australia made it a legal requirement to fit seat belts in newly manufactured cars, with this requirement coming into effect in Europe in 1965. In 1970, Victoria became the first in the world to make wearing seat belts compulsory for drivers and front-seat passengers.

With the worldwide introduction of front-seat passenger restraints in automobiles it is vitally important to ensure that the quality of craftsmanship of the restraints meets international standards.

To study the effectiveness of passenger restraint (seat-belt) systems, five popular brands were tested. To avoid any commercial confidentiality issues these brands have been randomly labelled system A, B, C, D, and E. For each system, a sample of five seat belts was randomly selected. The restraints were tested by measuring the forces at critical points on a test dummy when a vehicle was crashed into a barrier. The data

a) Given this data, test whether there is any evidence to suggest that there is a difference in the five systems in the event of a fatal injury occurring?

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b) State any and all of the assumptions you have made in part a). Where appropriate perform any relevant tests with a level of significance of 0.05. From a practical point of view could an alternative level of significance be considered?

c) Using Tukey's procedure, analyse the nature of the treatment effects by making all pairwise comparisons among the treatment means. Are your findings here consistent with those obtained in part a)?

d) Suppose that a car manufacturer is near the end of a contract that specifies that they must install seat belt restraint A into newly made cars. Test whether the remaining restraint systems provide equivalent safety results when compared with system A. Since the car manufacturer is near the end of the contract with system A, given these findings, would the company risk passenger safety by installing an alternative seat belt restraint? What other factors might impact upon a company's decision to install another restraint system?


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