Question

{Exercise 16.33} The following exercises require the use of a computer and software. Use a 5% significance level for all tests of hypotheses. Dataset: Distance Percent 7.5 68 8.3 66 6.2 34 1.6 30 5.6 70 6 62 4.3 47 8.1 72 5.7 40 0.3 53 1.6 18 2.5 48 5.8 53 5.3 48 6.3 64 3.4 52 6.2 61 3.2 34 6.3 65 6.1 66 4.6 33 6.7 76 0.5 34 3.2 46 5.3 55 5 33 4.8 46 6.4 49 0.2 17 4.9 47 6.2 63 7.6 69 6.6 54 2.9 52 2.1 43 4.8 35 8.1 58 1.2 5 4.6 46 4 57 6.1 40 0.8 39 5.9 42 6.5 62 6.5 52 7.5 76 7.2 67 6.7 45 4.1 23 4 33 4.8 59 4 50 6.2 49 5.5 44 7 52 7.5 68 6.2 48 5.7 55 7.3 77 1.9 9 2.8 35 6.3 51 9.4 84 3.7 30 4.9 61 1.8 40 3.6 24 2.9 37 2.6 51 3.1 30 4.7 47 5.9 54 2.5 47 4.6 52 5.2 52 7.6 52 3.7 33 7.4 74 3.3 56 5.1 53 5.1 54 7.5 76 4.7 37 2.7 45 2.7 50 Fire damage in the United States amounts to billions of dollars, much of it insured. The time taken to arrive at the fire is critical. This raises the question, Should insurance companies lower premiums if the home to be insured is close to a fire station? To help make a decision, a study was undertaken wherein a number of fires were investigated. The distance to the nearest fire station (in kilometers) and the percentage of fire damage were recorded. a)  Test to determine whether there is evidence of a linear relationship between distance to the nearest fire station and percentage of damage. Select one of the following: 1) There is evidence of a linear relationship between distance and fire damage 2) There is not enough evidence of a linear relationship between distance and fire damageItem 1 b)  Estimate the slope coefficient with 95% confidence (to 3 decimals). __________ +or- _________   c)  Determine the coefficient of determination (to 4 decimals). R2 = ________ d) What does this statistic tell you about the relationship? Select one of the following : 1) There is a weak linear relationship between distance and fire damage 2) There is a moderately strong linear relationship between distance and fire damage 3) There is a very strong linear relationship between distance and fire damage 4) There is no linear relationship between distance and fire damage

Answer 1

a) Correlation coefficient:

r= 0.707362

Hypothesis test to find evidence:

and

DF= N-2= 83

Test statistic:

P-value:0.000

The test statistic is significant and there is enough evidence to conclude that there is a relationship between two variables.

b) To calculate SLo

Percent= 23.11+5.347*Distance

To calculate the standard error for the slope:

95% confidence interval:

df=N-2=83

t critical: 1.9889598

CI: (5.347 - 1.9889598* 0.586, 5.347 + 1.9889598* 0.586)

CI: (4.180, 6.513)

C) Coefficient of determination:

d) r= 0.70362

It simply says, there is a moderatly strong relationship between two variables.