# Population is: crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor.

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1 Population is: crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor. Population parameter: median Variable being compared: insurance pay out (in dollars) Split by category: minor vs serious injury crashes Our Achieved Problem: What is the difference between the median insurance pay out (in dollars) of minor injury crashes compared with serious injury crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor. Many students forgot to put the population in their problem, and did not look up the correct description for the category split. Suggest: Students practice writing problems and check they have everything required in them. 1 P a g e

2 Our Merit Problem: Adding research and prediction Introduction: explaining the context after researching. It would be reasonable to suspect that a car crash that causes a serious injury would also result in damage to the vehicles involved. This document provides us with three types of injury. Fatal injuries: injuries that result in death within 30 days of the crash. Serious injuries: fractures, concussions, internal injuries, crushings, severe cuts and lacerations, severe general shock necessitating medical treatment and any other injury involving removal to and detention in hospital. Minor injuries: injuries of a minor nature such as sprains and bruises. In light of these definitions I can predict that a car crash that results in a minor injury in unlikely to incur a massive insurance pay out for repairs. Given that a minor injury does not involve hospital, so this excludes broken bones, these must be reasonably low impact crashes. What is the difference between the median insurance pay out (in dollars) of minor injury crashes compared with serious injury crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor. I predict that there will be a difference, and that serious injury crashes also result in more expensive car repair costs. I predict this because an accident which results in a person requiring medical attention at a hospital would logically require more car repair costs. 2 P a g e

3 Our Excellence Problem: adding some evidence of statistical insight and a clear purpose. Introduction: explaining the context after researching. It would be reasonable to suspect that a car crash that causes a serious injury would also result in damage to the vehicles involved. This document provides us with three types of injury. Fatal injuries: injuries that result in death within 30 days of the crash. Serious injuries: fractures, concussions, internal injuries, crushings, severe cuts and lacerations, severe general shock necessitating medical treatment and any other injury involving removal to and detention in hospital. Minor injuries: injuries of a minor nature such as sprains and bruises. The first thing I noticed was that my sample does not include fatal injuries. I notice the drivers were interviewed, and realise that this would exclude drivers that were deceased. In light of these definitions I can predict that a car crash that results in a minor injury in unlikely to incur a massive insurance pay out for repairs. Given that a minor injury does not involve hospital, so this excludes broken bones, these must be reasonably low impact crashes. Clear purpose: linking my research with my comparative question. Insurance companies may be interested in the difference in payout between minor injury crashes and serious injury crashes. They may use this information to modify and create insurance policies. What is the difference between the median insurance pay out (in dollars) of minor injury crashes compared with serious injury crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor. I predict that there will be a difference, and that serious injury crashes also result in more expensive car repair costs. I predict this because an accident which results in a person requiring medical attention at a hospital would logically require more car repair costs. Some statistical insight thoughts. Why would the insurance company pay out when alcohol or drugs were a factor? What is the total cost of repairs for all cars involved in the crash? What proportion of the total cost did the insurance company pay? What does this variable include? Hospital costs? Courtesy cars? Damage to other property? 3 P a g e

4 Plan: Tuesday, May 21, 2013: In V2U so no computers. Data: Analysis: What can we see? There are more minor injury crashes than serious injury crashes. Serious injury crashes have a wider range of insurance payout amouts, and the box is further up the scale, with no overlap. This tells me that there is a significant difference between the insurance payout for serious and minor injury crashes. Summary of Insurance.payout by Crash.severity Min. 1st Qu. Median Mean 3rd Qu. Max. Std.dev Sample.Size M S Putting the statistics into sentences, link to boxplots and context: Out of the 1409 crashes our sample includes 317 (about 22% of them). The standard deviation of serious injury crashes is over 3.5 times that of minor injury crashes. This confirms what we can see in the graph; serious injury crashes have more variation in their insurance pay-out than minor crashes. The range of minor injury crashes in \$12,030, compared to the range of serious injury crashes of \$28,930. So the range for serious crashes is more than double (2.4 times) the range of minor injury crashes. We can clearly see this on the box plot. 4 P a g e

5 Conclusion: Returning to my question: What is the difference between the median insurance pay out (in dollars) of minor injury crashes compared with serious injury crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor. I produced bootstrap confidence intervals for the mean and median difference due to crash severity of insurance pay-out amount. I did this as a double check and also to cater to people who understand and prefer means over medians. Neither of these intervals contain zero so I can make a call. It is a fairly safe bet that the difference between the median insurance pay out (in dollars) of minor injury crashes compared with serious injury crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor is between \$4551 and \$ It is a fairly safe bet that the difference between the mean insurance pay out (in dollars) of minor injury crashes compared with serious injury crashes in New Zealand in 2011 where drugs or alcohol were recorded as a factor is between \$ and \$ P a g e

6 6 P a g e Tuesday, May 21, 2013: In V2U so no computers.

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