Question

Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let µ denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: µ = 20 versus Ha: µ > 20 based on a sample of 15 observations gave t = 3.1. What conclusion is appropriate at each of the following significance levels?

(a) alpha= .05
a. Reject H0
b. Fail to reject H0

(b) alpha = .01
a. Reject H0
b. Fail to reject H0

(c) alpha = .001
a. Reject H0
b. Fail to reject H0

Answer 1

The critical value we need to compare the test statistic to has 15-1 = 14 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.