1. Some insurance companies claim that the rate of serious and fatal accidents is higher when the car size is smaller, and therefore question the policy of offering reduced rates to owners of small cars. To investigate this, a researcher analyzed a sample of Queensland accident data provided by RACQ, with the results shown in the table below:
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|
|
Car Type
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|
|
Injury type
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Small
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Medium
|
Large
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|
Fatal
|
32
|
14
|
16
|
|
Serious
|
29
|
32
|
34
|
|
Minor
|
59
|
83
|
105
|
2. Assume that the level of significance used to test if there is a relationship between the type of car and injury type is 0.025.
1. Compute the expected frequency under the null hypothesis for the number of minor injuries experienced from small cars, giving your answer correct to two decimal places.
2. Calculate the test statistic, reporting your answer correct to three decimal places.
3. Use the tables in the text to determine the critical value for the test.
4. Is the null hypothesis rejected for this test? Type yes or no.
5. Hence, on the basis of this test, does there appear to be a relationship between the type of injury sustained in an accident and the type of car driven? Type yes or no.