Waterbury Insurance Company wants to study the relationship between the amount o
ID: 3257925 • Letter: W
Question
Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (X) and the amount of fire damage, in thousands of dollars (Y). The MegaStat output is reported below.
Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?
How much damage would you estimate (in dollars) for a fire 7 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)
Fill in the blank below. (Round your answer to 1 decimal place.)
State the decision rule for .01 significance level: H0 : = 0; H1 : 0. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
Is there any significant relationship between the distance from the fire station and the amount of damage? Use the .01 significance level.
Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (X) and the amount of fire damage, in thousands of dollars (Y). The MegaStat output is reported below.
Explanation / Answer
a-1) Y (damage) = 13.4045 + 4.6357 X (Distance)
a-2) The relation shipe between distance and dmage is direct relation
since slope = 4.6357 which is > 0 (positive)
b) Estimated damage (Y) = 13.4045 + 4.6357 (7) = 45.8544
c-1) Coefficient determination r^2 = 1810.5782/3076.0716 = 0.5886
c-2) 58.86% of the variation in damage is explained by variation in distance
d-1) Coefficient of correlation rxy = 0.7672
d-2) There is a fairly solid direct between the variables.
since slope = 4.6357 which is > 0 (positive)
e-1) Reject H0 if t < -2.763 or t > 2.763
e-2) Test statistic t = 4.6357/7.322 = 0.63312
e-3) Here t value > t critical value, so we reject H0
Thus we conclude that There is significantsignificant relationship between distance and fire damage.
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