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* = 15, *t* = 3.1,
*α* = 0.05

*P*-value = ???

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* = 1.6,
*α* = 0.01

*P*-value = ???

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 = ???

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Answer #1

Solution:

Given that,

a)

df = 14

p-value = 0.004

The p-value is p = 0.004, and since p = 0.004 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

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

than 20.

b)

df = 9

p-value = 0.072

The p-value is p = 0.072, and since p = 0.072 > 0.01, it is concluded that the null hypothesis is fail to reject.

Conclusion:

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)

df = 24

p-value = 0.689

The p-value is p = 0.689.

Conclusion:

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading

higher than 20.

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.)
(a) n =...

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.)
(a) n =...

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.)
(a) z =...

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