Question

U.S. Department of Transportation As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Your first step in the analysis is to construct a scatterplot of the data. FIGURE. SCATTERPLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear regression analysis. The results are as follows:

The p-value for "Percent under 21" in the regression output is p = 0.0000. The t test for significance in simple linear regression is

H₀: β₁ = 0
H_a: β₁ ≠ 0

Use alpha = .05. What does the p-value tell you about the estimated regression line?

p = 0.0000 indicates that the slope of the estimated regression line is not zero, a significant relationship exists between the two variables, and H0 should be rejected.

p = 0.0000 indicates that the slope of the estimated regression line is zero, a significant relationship does not exist between the two variables, and H0 should be rejected.

p = 0.0000 indicates that the slope of the estimated regression line is zero, a significant relationship does not exist between the two variables, and H0 should not be rejected.

p = 0.0000 indicates that the slope of the estimated regression line is not zero, a significant relationship exists between the two variables, and H0 should be not be rejected.

Answer 1

Given that, the null and alternative hypotheses for the slope test are,

Null Hypothesis : H0: β1 = 0
Alternative Hypothesis : Ha: β1 ≠ 0

p-value for this test is, p = 0.0000

Since, p-value = 0.0000 is less than 0.05 level of significance, we reject the null hypothesis (H0) and conclude that the the slope of the estimated regression equation is different from zero.

Answer : p = 0.0000 indicates that the slope of the estimated regression line is not zero, a significant relationship exists between the two variables, and H0 should be rejected.