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 u denote the true average reflectometer reading for a new type of paint under consideration. A test of Ho: 20 versus Ha: u 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 17 z 3.1 a 0.05 P-value State the conclusion in the problem context. eject 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. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (b) n 3 7, z 1.7, a 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. 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 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

a) p-value = P(Z > 3.1) = 1 - P(Z < 3.1) = 1 - 0.9990 = 0.0010

Option-B)

b) p-value = P(Z > 1.7) = 1 - P(Z < 1.7) = 1 - 0.9554 = 0.0446

Option-C)

c) p-value = P(Z > -0.7) = 1 - P(Z < -0.7) = 1 - 0.2420 = 0.7580

Option-C)

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