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 under 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.) (a) n = 14, z = 3.2, alpha = 0.05 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. 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. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (b) n = 10, z = 1.8, alpha = 0.01 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 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 not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (c) n = 24, z = -0.3 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.

Explanation / Answer

a) This is a one tailed test.

p value = 0.000687.

As p value is less than 0.05 so we reject the null hypothesis.

Answer is option B)

b)

P value = 0.03593.

As p value is greater than 0.01 so we fail to reject the null hypothesis.

Answer is option D)

c)

p value = 0.382089.

As p value is greater than 0.05 so we fail to reject the null hypothesis.

Answer is option C)

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