Question

An insurance agent says the standard deviation of the total hospital charges for patients involved in a crash in which the vehicle struck a construction barricade is less than ​$4000. A random sample of 25total hospital charges for patients involved in this type of crash has a standard deviation of ​$4400. At α=0.01
can you support the​ agent's claim? Use the​ P-value method to test the claim

Answer 1

Let the null hypothesis be that the agent's claim is correct. Using a standard normal probability table we find:
$p-value=P(Z \ \textgreater \ 1.1)=0.14$
The p-value 0.14 is much larger than alpha = 0.01, so we cannot reject the agent's claim.