A fire insurance company wants to examine the relationship between the amount of

Question

A fire insurance company wants to examine the relationship between the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. A sample of 15 recent fires in a particular city was taken. The amount of damage to the house (in thousands of dollars) and the distance from the burning house to the nearest fire station (in miles) were recorded. Part of the output from a simple linear regression analysis is given below. Assume all conditions are met for simple linear regression inference. A hypothesis test is to be performed to determine if the distance from the nearest fire station is a significant predictor of amount of damage. Which of the following is the correct conclusion based on the results of the hypothesis test? Click the icon to view the regression analysis. Choose the correct answer below. A. There is suggestive evidence to indicate that the distance from the nearest fire station is a significant predictor of the amount of damage (t-statistic = 2.337, dof = 13, P-value = 0.018) B. There is suggestive, but weak evidence to indicate that the distance a from the nearest fire station is a significant predictor of the amount of damage statistics (t-statistic = 2.337, dof = 14, P-value = 0.051) C. There is suggestive, but weak evidence to indicate that the distance a from the nearest fire station is a significant predictor of the amount of damage (t-statistic = 2.137, dof = 13, P-value = 0.052). D. There is strong evidence to indicate that the distance from the nearest fire station s a significant predictor of the amount of damage (t-statistic = 2.137, dof = 13, P-value = 0.052) E. There is not enough evidence to indicate that the distance from the nearest fire station is a significant predictor of the amount of damage (t-statistic = 1.403, dof = 14, P-value = 0.182)

Explanation / Answer

t-statistic = 3.554/1.663 = 2.137

Degrees of freedom = n - 2 = 15 - 2 = 13

So,

p - Value = 2*P(t > 2.137) = 2*0.0261 = 0.052

Hence,

Option C is correct.

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