Question

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 *H*_{0}: *μ* = 20 versus
*H*_{a}: *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) *z* = 3.2, *α* =
0.05

*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. 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) *z* = 1.8, *α* =
0.01

*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 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.Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(c)

* z* = −0.5

, *α* = 0.10

*P*-value =

State the conclusion in the problem context.

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. 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.

You may need to use the z table to complete this problem.

Answer #1

Decision rule: If p-value is less than alpha, reject the null hypothesis

a) p-value = P(Z > 3.2) = 0.0007

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

b) p-value = P(Z > 1.8) = 0.0359

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) p-value = P(Z > -0.5) = 0.6915

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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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
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a random sample of size n from a normal population
distribution. What conclusion is appropriate in each of the
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