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 $3800. a random sample of 20 total hospital charges for patients involved in this type of crash has a standard deviation of $4200. at α = 0.05 can you support the agents claim? use the p - value method to test the claim.

$h_{a}:\sigma > $3800$ $h_{a}:\sigma < $3800$

identify the standardized test statistic.
23.21 (round to two decimal places as needed.)

identify the p - value.
0.772 (round to three decimal places as needed.)

choose the correct conclusion belo
a. reject $h_{0}$. there is enough evidence at the 5% level of significance to support the insurance agents claim.

b. fail to reject $h_{0}$. there is not enough evidence at the 5% level of significance to support the insurance agents claim.

c. reject $h_{0}$. there is not enough evidence at the 5% level of significance to support the insurance agents claim.

d. fail to reject $h_{0}$. there is enough evidence at the 5% level of significance to support the insurance agents claim.

Explanation:

1. Recall the decision rule for hypothesis testing using the P - value method: If the P - value \(>\alpha\) (here \(\alpha = 0.05\)), we fail to reject the null hypothesis \(H_0\).
2. The given P - value is \(0.772\), and \(0.772>0.05\).
3. When we fail to reject \(H_0\), it means there is not enough evidence at the \(\alpha = 0.05\) level of significance to support the alternative hypothesis (which is the insurance agent's claim that \(\sigma<\$3800\)).

Answer:

B. Fail to reject \( H_0 \). There is not enough evidence at the 5% level of significance to support the insurance agent's claim.