statistics help

Question

Experience in investigating insurance claims shows that the average cost to process a claim is approximately normally distributed with a mean of $80. New cost-cutting measures were started and a sample of 25 claims was tested. The sample mean of the costs to process these claims was %76 and the sample standard deviation of the costs was $10. We would like to test whether the cost-cutting measures seem to be working at the 5% significance level.
A. State the null and alternative hypotheses for this test.
B. find the critical value for this test.
C. Calculate the test statistic.
D. Should we reject or fail to reject the null hypothesis?
E.Based on your answer to a-d, what is your conclusion about the cost cutting measures?

Answer 1

a)  H₀: the mean is 0 and H_A: the mean is not 0.

 

b) the critical value is 1.96 at the 5% level of significance.

 

c) z = (80 - 76)/(10/sqrt(25)) = 4/2 = 2.00

 

d) Since z = 2.00 > 1.96, we can reject the null hypothesis.

 

e) There is enough evidence to show that the average cost to process a claim is approximately normally distributed with a mean of $80.