The paint used to make lines on roads must reflect enough light to be clearly vi

Question

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: = 20 versus Ha: > 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 = 11, t = 3.1, = 0.05
P-value =  

State the conclusion in the problem context.

(b)    n = 8, t = 1.8, = 0.01
P-value =  

State the conclusion in the problem context.

(c)    n = 26,

t = 0.7

P-value =  

State the conclusion in the problem context.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

a)

As this is right tailed, and df = n - 1 = 10, then the P value of t = 3.1 is

P = 0.005625329 [ANSWER]

As P < 0.05, we reject Ho.

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

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b)

In this case, df = n - 1 = 7, and t = 1.8, so

P = 0.057442227

As P > 0.01, we fail to reject Ho.

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, C]

**********************

C)

Here, df = 25, and t = -0.7, so the right tailed P value is

P = 0.754804732

Thus,

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, A]

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