The paint used to make lines on roads must reflect enough light to be clearly vi
ID: 3429288 • 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 = 18, t = 3.2, ? = 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 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 = 1.7, ? = 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.
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 = 29, t = ?0.2
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 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.
Explanation / Answer
(a) The degree of freedom =n-1=18-1=17
It is a right-tailed test.
So the p-value= P(t with df=17>3.2) =0.003 (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.
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(b) The degree of freedom = 10-1=9
So the p-value= P(t with df=9 >1.7)= 0.062 (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.
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(c) The degree of freedom =29-1=28
So the p-value= P(t with df=28 >?0.2) =0.579 (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.
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