Question

# The paint used to make lines on roads must reflect enough light to be clearly visible...

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? (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.

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.

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