Paint used to paint lines on roads must reflect enough light to be clearly visib
ID: 3435401 • Letter: P
Question
Paint used to paint 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 based on a sample of 13 observations gave t = 3.1. What conclusion is appropriate at each of the following significance levels?
(a) ? = 0.05
Reject H0
Fail to reject H0
(b) ? = 0.01
Reject H0
Fail to reject H0
(c) ? = 0.001
Reject H0
Fail to reject H0
Explanation / Answer
The critical value we need to compare the test statistic to has 13-1 = 12 degrees of freedom. Since it is a one tailed test (the alternative hypothesis is one directional) then only one tail will contain the entire alpha value.
A) critical value = 1.761
Reject Ho since test statistic is larger than the critical value
B) critical value = 2.624
Reject Ho since test statistic is larger than the critical value
C) critical value = 3.787
Do not reject Ho since the test statistic is less than the critical value.
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