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 H_a: 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?
(Round your P-values to three decimal places.)

(a)    z = 3.2, α = 0.05
P-value =  

State the conclusion in the problem context.

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.     Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(b)    z = 1.8, α = 0.01
P-value =  

State the conclusion in the problem context.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.     Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(c)    

z = −0.5

, α = 0.10
P-value =  

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.     Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

You may need to use the z table to complete this problem.

Answer 1

Decision rule: If p-value is less than alpha, reject the null hypothesis

a) p-value = P(Z > 3.2) = 0.0007

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20

b) p-value = P(Z > 1.8) = 0.0359

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20

c) p-value = P(Z > -0.5) = 0.6915

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20