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* = 19, *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.

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 sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(b) *n* = 9, *t* = 1.6,
*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.

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.

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

(c) *n* = 26, *t* =
−0.3

*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.

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.

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

Answer #1

Ans:

a)(a) n = 19, t = 3.3, α = 0.05

df=19-1=18

P-value = tdist(3.3,18,1)=**0.002**

b) n = 9, t = 1.6, α = 0.01

df=9-1=8

P-value =tdist(1.6,8,1)=**0.074**

c) n = 26, t = −0.3

df=26-1=25

P-value =tdist(0.3,25,1)**=0.383**

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