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)    n = 17, t = 3.3, α = 0.05
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.

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.

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

(b)    n = 10, t = 1.7, α = 0.01
P-value =

State the conclusion in the problem context.

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.    

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.

(c)    n = 25,

t = −0.5

P-value =

State the conclusion in the problem context.

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.    

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.

Answer 1

This is the right tailed test .

(a)

n = 17, t = 3.3, α = 0.05

P-value = P(t₁₆ > 3.3) = 0.002

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint

has a reflectometer reading higher than 20.

(b)

n = 10, t = 1.7, α = 0.01

P-value = P(t₉ > 1.7) = 0.062

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)

n = 25,

t = −0.5

P-value = P(t₂₄ > -0.5) = 0.689

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