Question

Start with the Excel spreadsheet Insurance Company

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 about per claim was $4,800 with a standard deviation of $1,300. Does it appear that prevention plans were effective in reducing the mean amount of a claim? Use a 0.05 significance level. Use this information to determine the following questions based on sampled means:

A. What is the null hypothesis statement for this problem?

B. What is the alternative hypothesis statement for this problem?

C. What is alpha for this analysis?

D. What is the most appropriate test statistic for this problem (choose one of the following)

a. T

b. Z

E. What is the value of the test statistic for the most appropriate analysis?

F. What is the lower bound value of the critical value? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

G. What is the upper bound value of the critical value? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

H. Is it reasonable to conclude that the prevention plan was effective in reducing the mean amount of a claim? (choose one of the following)

a. Yes

b. No

I. What is the p-value for this analysis? (Hint: Use this value to double check your conclusion)

Answer 1

A) H0: = 5000

B) H1: < 5000

C) = 0.05

D) Z test statistic

E) Z =

= -2.18

F) For alpha = 0.05, the critical value is z_0.05 = -1.645

G) N/A

H) As the test statistic value is less than the critical value, so the null hypothesis will be rejected.

Yes, it is reasonable to conclude that the prevention plan was effective in reducing the mean amount of claim.

I) P-value = P(Z < -2.18)

= 0.0146