posted by Scott on .
a) 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 70 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 56 IHI policyholders aged 25 or older. The data from these samples is displayed in the table.
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.
Accidents Age Total
< 25 ¡Ý 25
< 2 46 37 83
¡Ý 2 24 19 43
Total 70 56 126
b) Using the test statistic for IHI's hypothesis test and a 95% confidence level, IHI should (accept, reject or retain) the null hypothesis.
We do not have the table, and I am not familiar with some of the symbols you are using.