Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.
Before: | 11 | 23 | 65 | 117 | 62 | 66 |
After: | 12 | 22 | 43 | 81 | 75 | 75 |
(a) The article included the statement "A paired t test
was performed to determine whether there was any change in the mean
number of crashes before and after the addition of distance
information on the signs." Carry out such a test. [Note:
The relevant normal probability plot shows a substantial linear
pattern.]
State and test the appropriate hypotheses. (Use
α = 0.05.)
H0: μD =
0
Ha: μD ≥ 0
H0: μD =
0
Ha: μD >
0
H0: μD =
0
Ha: μD ≤ 0
H0: μD =
0
Ha: μD ≠ 0
H0: μD =
0
Ha: μD < 0
Calculate the test statistic and P-value. (Round your test
statistic to two decimal places and your P-value to three
decimal places.)
t | = | |
P-value | = |
State the conclusion in the problem context.
Reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
Fail to reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
Reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
(b) If a seventh site were to be randomly selected among locations
bearing service signs, between what values would you predict the
difference in number of crashes to lie? (Use a 95% prediction
interval. Round your answers to two decimal places.)
,
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