Question

The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a standard deviation of 0.04. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.04, Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. P KQ 0 Oso X X a Р S 00 020​

Answer 1

The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.

The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.

Mathematically, the null and alternative hypotheses can be expressed as follows:

H0: σ = 0.04

Ha: σ ≠ 0.04

where σ represents the standard deviation of the number of accidents per day.

The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.