An insurance company suspects that there is a positive linear relationship between the dollar amount of fire damage in residential fires, and the distance between the residence and the nearest fire station. Data were collected on a random sample of 17 residential fires and the results are given below. The amount of fire damage (in thousands of dollars) is denoted as cost, and the distance between the residence and the nearest fire station (in miles) is denoted as distance.
Cost Distance
26 1.5
27 2.6
28 3.7
37 3.8
38 4.3
47 4.5
48 4.9
50 5.8
52 6.5
57 6.8
59 7.5
68 7.6
70 8.4
83 8.5
84 9.3
96 9.4
98 9.9
a. Test the appropriate hypothesis at the .10 level of significance. Make sure that ALL the steps of the hypothesis testing process are clearly identified in the appropriate order. Note that the value of the test statistic has to be obtained from the Excel output, NOT calculated by hand.
b. Using Excel, generate a 90% interval for the dollar amount of fire damage for a residence that is 5.7 miles from the nearest fire station. (You have to decide if the interval is a confidence interval or a prediction interval) From: __________________ To: ________________
c. Using Excel, generate a 99% interval for the average dollar amount of fire damage for residences that are 4.4 miles from the nearest fire station. (You have to decide if the interval is a confidence interval or a prediction interval) From: __________________ To: ________________
NOTE: The confidence or prediction intervals in parts b and c must be obtained from the Excel output, NOT calculated by hand.