Question

The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0016 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0016 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.

Answer 1

H0: σ² = 0.0016 against the claim

H1: σ² ≠ 0.0016

Explanation:

The claim is the alternative hypothesis . If we have the alternative hypothesis that variance is not equal to 0.0016. Then the null hypothesis would

H0: σ² = 0.0016 against the claim

H1: σ²≠ 0.0016

This is a two tailed test.

The null hypothesis is opposite to the claim stated. The claim is the alternative hypothesis.

By knowing the alternative hypothesis one can find the null hypothesis.

The claim is that the variance of the number of accidents per day is no longer equal to 0.0016.

The claim is H1: variance≠ 0.0016 or

H1= σ²≠ 0.0016

Therefore the null hypothesis is

H0: σ²=0.0016