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 = 15, t = 3.1, α = 0.05
P-value = ???

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 = 1.6, α = 0.01
P-value = ???

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 = ???

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

Answer 1

Solution:

Given that,

a)

df = 14

p-value = 0.004

The p-value is p = 0.004, and since p = 0.004 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

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

than 20.

b)

df = 9

p-value = 0.072

The p-value is p = 0.072, and since p = 0.072 > 0.01, it is concluded that the null hypothesis is fail to reject.

Conclusion:

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)

df = 24

p-value = 0.689

The p-value is p = 0.689.

Conclusion:

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

higher than 20.