Question

The paint used to make 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 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations?

(a) n = 14, t = 3.1, α = 0.05

(b) n = 10, t = 1.8, α = 0.01

Answer 1

a.) t calc = 3.1
t-table = 1.77
Since the t-calc > t-table, we reject H0 and accep HA.
We conclude that the true average refrectometer reading is greater than 20.

b.) t-calc = 1.8
t-table = 2.82
Since t-calc < t-table, we fail to reject H0.
We conclude that the true average refrectometer reading may be 20.