Paint used to paint lines on roads must reflect enough light

Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let ? denote the true average reflectometer reading for a new type of paint under consideration. A test of H₀: ? = 20 versus H_a: ? > 20 based on a sample of 13 observations gave t = 3.1. What conclusion is appropriate at each of the following significance levels?

(a)    ? = 0.05

Reject H₀

Fail to reject H₀    

(b)    ? = 0.01

Reject H₀

Fail to reject H₀    

(c)    ? = 0.001

Reject H₀

Fail to reject H₀

Solution

The critical value we need to compare the test statistic to has 13-1 = 12 degrees of freedom. Since it is a one tailed test (the alternative hypothesis is one directional) then only one tail will contain the entire alpha value.

A) critical value = 1.761
Reject Ho since test statistic is larger than the critical value

B) critical value = 2.624
Reject Ho since test statistic is larger than the critical value

C) critical value = 3.787
Do not reject Ho since the test statistic is less than the critical value.