Question

The State Department of Transportation proposes to redesign the signs on all the state highways such that they are easier to read from a greater distance. The Department's hypothesis is that maximum reading distance in feet (Y) decreases as age (X) increases. The proposal, which is going to cost millions of dollars, is supposed to improve highway safety for older drivers. An independent research firm is hired to study the relationship between age and maximum sign legibility distance (in feet). The firm estimates the regression equation below for a sample of 100 drivers ranging in age from 18 to 80. LaTeX: \hat Y Y ^ = 590 - 3.4x, with a standard error of the slope for x of .54. The RLaTeX: ^2 2 = 66.6% Where LaTeX: \hat Y Y ^ = distance and x = driver age Is there a relationship between age and sign legibility distance?

Answer 1

Let denotes the slope for the regression equation to predict maximum sign legibility distance using age as a predictor.

To test against

Given

The test statistic can be written as

which under H₀ follows a t distribution with n-2 df.

We reject H₀ at 5% level of significance if p-value < 0.05

Now,

The value of the test statistic =

and P-value

Since P-value < 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that there is enough evidence to support the claim that maximum reading distance in feet (Y) decreases as age (X) increases.