The paint used to make lines on roads must reflect enough light to be clearly vi
ID: 3429505 • Letter: T
Question
The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let ? denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: ? = 20 versus Ha: ? > 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 = 12, t = 3.2, ? = 0.05
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.
(b) n = 10, t = 1.6, ? = 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 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.
(c) n = 25,
t = ?0.4
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 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.
Explanation / Answer
It is a right-tailed test.
(a) n = 12, t = 3.2, ? = 0.05
The degree of freedom=n-1=12-1=11
P-value = P(t with df=11>3.2) =0.0042 (from student t table)
Since the p-value is less than 0.05, we reject Ho.
Answer: 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, ? = 0.01
The degree of freedom =n-1=10-1=9
P-value = P(t with df=9 >1.6) =0.0720 (from student t table)
Since the p-value is larger than 0.01, we do not reject Ho.
Answer:
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 = ?0.4
The degree of freedom =n-1=25-1=24
p-value= P(t with df=24 > -0.4)=0.6537 (from student t table)
Answer: Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.