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 mu denote the true average reflectometer reading for a new type of paint consideration. A test of H_0: mu = 20 versus H_a: mu > 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.) n = 17, t = 3.3, alpha = 0.05 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. 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. n = 7, t = 1.7, alpha = 0.01 P-value = State the conclusion in the problem context. 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. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. n = 25, t = -0.7 P-value = State the conclusion in the problem context. 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. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Explanation / Answer

As we can see, this is a right tailed t test.

a)

Hence,

df = n - 1 = 16

Thus, using technology,

P(t > 3.3) = 0.002259651 [ANSWER, P VALUE]

Hence, as P < 0.05, we reject Ho. [OPTION C, ANSWER]

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b)

Hence,

df = n - 1 = 6

Thus, using technology,

P(t > 1.7) = 0.070019827 [ANSWER, P VALUE]

Hence, as P > 0.01, we fail to reject Ho. [OPTION C, ANSWER]

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c)

Hence,

df = n - 1 = 24

Thus, using technology,

P(t > -0.7) = 0.754671197 [ANSWER, P VALUE]

Hence, as P is very large, we fail to reject Ho. [OPTION B, ANSWER]

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