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 = 19, 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.

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 sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(b)    n = 9, t = 1.6, 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.

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.

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

(c)    n = 26, t = −0.3

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.

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.

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

Answer 1

Ans:

a)(a)    n = 19, t = 3.3, α = 0.05

df=19-1=18
P-value = tdist(3.3,18,1)=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 = 9, t = 1.6, α = 0.01

df=9-1=8
P-value =tdist(1.6,8,1)=0.074

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 = 26, t = −0.3

df=26-1=25

P-value =tdist(0.3,25,1)=0.383

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