Question

an insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is $5,000. after introducing several plans to prevent loss, it randomly samples 200 policyholders and finds the mean amount per claim was $4,800 with a standard deviation of $1,300.does it appear the prevention plans were effective in reducing the mean amount of a claim? use the 0.05 significance level.a. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.)

Answer 1

To determine if the prevention plans were effective in reducing the mean amount of a claim, a hypothesis test needs to be performed. The null hypothesis is that the mean amount per claim is equal to $5,000, and the alternative hypothesis is that the mean amount per claim is less than $5,000.

Step-by-step explanation:

To determine if the prevention plans were effective in reducing the mean amount of a claim, we need to perform a hypothesis test. The null hypothesis (H0) is that the mean amount per claim is equal to $5,000, and the alternative hypothesis (H1) is that the mean amount per claim is less than $5,000.

To perform the hypothesis test, we need to find the test statistic and compare it to the critical value at the 0.05 significance level. The test statistic is calculated using the sample mean, the population mean, the standard deviation, and the sample size.

If the test statistic is less than the critical value, we reject the null hypothesis and conclude that the prevention plans were effective in reducing the mean amount of a claim. If the test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis.