Question

An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. They are concerned that the true mean does not equal this because they could potentially lose a lot of money. They randomly select 40 claims, and calculate the sample mean of $1,950. Assuming that the standard deviation of claims follows a Normal distribution with known standard deviation $500, perform a hypothesis testing to see if the insurance company should be concerned.

What is the correct and most appropriate conclusion?

For any hypothesis testing problem, there is always a chance that “a correct null hypothesis is
incorrectly rejected”. In other words, when the null hypothesis is true, what is the probability that
the above Z-test procedure will incorrectly reject a correct null hypothesis?

Answer 1

Solution:

Set null and alternative hypothesis:

H0:

Ha:

alpha=0.05

Test statistic:

z=xbar-mu/sigma/sqrt(n)

=(1950-1800)/(500/sqrt(40)

z=1.897

p value in excel is

=2*(1-righ taill prob)

Right tail prob

==NORMSDIST(1.897)

=0.971086031

=2*(1-0.971086031)

=0.057827938

p=0.0578

p>0.05

Fail to reject null hypothesis

e correct and most appropriate conclusion

There is no sufficient statistical evidence at 5% level of significance to conclude that  true mean  claim amount is not equal to $1800

he probability that
the above Z-test procedure will incorrectly reject a correct null hypothesis is called type 1 error and denoted by alpha

Here alpha=0.05

so

he probability that
the above Z-test procedure will incorrectly reject a correct null hypothesis is 0.05