Demographics and Population Statistics
Police reports and insurance claims indicate that the mean loss during a residential break-in is $1381. Actuaries working for Eagle Pacific Insurance Company need to check whether the mean loss has changed during the past year in order to determine new policy rates. A random sample of 17 residential break-ins was obtained, and the loss due to each burglary was recorded. The sample mean loss (in dollars) was 1857 and the standard deviation was σ = 786. Assume the loss distribution is normal and use a = 0.05.
a. Is there any evidence to suggest the true mean loss as a result of a residential break-in has changed?
b. Find bounds on the p value associated with this hypothesis test.
c. Carefully sketch a graph illustrating the p value and the value of the test statistic.