I need to understand this problem , help me please The paint used to make lines
ID: 3124408 • Letter: I
Question
I need to understand this problem , help me please
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 = 11, t = 3.1, = 0.05
P-value =?
(b) n = 8, t = 1.6, = 0.01
P-value =?
(c) n = 21, t = 0.7
P-value =?
Explanation / Answer
a)
As Ha: u < 20, then we see that this is a right tailed test.
Also, df = n - 1 = 10.
Using technology to get the right tailed P value of t = 3.1,
Pvalue = 0.005625329 [ANSWER]
As P < 0.05, we Reject Ho. There is significant evidence that the mean is greater than 20 at 0.05 level. [CONCLUSION]
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B)
As Ha: u < 20, then we see that this is a right tailed test.
Also, df = n - 1 = 7.
Using technology to get the right tailed P value of t = 1.6,
Pvalue = 0.076815854 [ANSWER]
As P > 0.01, we fail to Reject Ho. There is no significant evidence that the mean is greater than 20 at 0.01 level. [CONCLUSION]
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c)
As Ha: u < 20, then we see that this is a right tailed test.
Also, df = n - 1 = 20.
Using technology to get the right tailed P value of t = -0.7,
Pvalue = 0.754004891 [ANSWER]
As this is very large, we fail to Reject Ho. There is no significant evidence that the mean is greater than 20. [CONCLUSION]
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*Since this is a right tailed test, if you are using Excel, you can type
=1-T.DIST(t value, degrees of freedom, 1)
to get the P values here.