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) *n* = 17, *t* = 3.3,
*α* = 0.05

*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.

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.

(b) *n* = 10, *t* = 1.7,
*α* = 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 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.

(c) *n* = 25,

* t* = −0.5

*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.

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.

Answer #1

This is the right tailed test .

(a)

n = 17, t = 3.3, α = 0.05

P-value = P(t_{16} > 3.3) = 0.002

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint

has a reflectometer reading higher than 20.

(b)

n = 10, t = 1.7, α = 0.01

P-value = P(t_{9} > 1.7) = 0.062

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 = 25,

t = −0.5

P-value = P(t_{24} > -0.5) = 0.689

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 H0: μ = 20
versus Ha: 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.)
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The paint used to make lines on roads must reflect enough light
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average reflectometer reading for a new type of paint under
consideration.
A test of H0: μ = 20 versus
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random sample of size n from a normal population
distribution.
What conclusion is appropriate in each of the following
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(Round your P-values to three decimal places.)
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