IHI insurance is interested in determining whether younger drivers (below the age of 25) are more prone to motor accidents than older drivers (25 or older). A random sample of 68 IHI policyholders below the age of 25 were selected and whether they had been in less than 2 (or 2 or more) motor accidents in the past year was recorded. This process was repeated for a random sample of 48 IHI policyholders aged 25 or older. The data from these samples is displayed in the table.
You may find this chi-square distribution table useful throughout the following questions.
a)The IHI statisticians would like to test whether the proportion of policyholders who have had at least 2 accidents in the past year is the same for those who are aged below 25 (<25) and those who are aged 25 or older (¡Ý25). They have constructed a hypothesis test with H0: <25 = ¡Ý25 and H1: <25 ¡Ù ¡Ý25. Calculate the test statistic (¦Ö2) that corresponds to this hypothesis test. Give your answer to 3 decimal places.
¦Ö2 =
Accidents Age Total
< 25 ¡Ý 25
< 2 47 32 79
¡Ý 2 21 16 37
Total 68 48 116
1 answer