Question

Before: 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. 16 27 65 123 57 65 After: 17 25 44 75 74 (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 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 a = 0.05.) Hoi Hp = 0 H: 420 Ho: Mo - 0 H: UD SO Ho: MD = 0 H:Hp > 0 Mo: 4 - 0 Ho Mp = 0 H.: Hp < 0 Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your p-value to three decimal places.) P-value= State the conclusion in the problem context. Reject Ho. 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 Ho. The data suggests a significant mean difference in the average number of accidents after information was added to road signs. Fail to reject Ho. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs. Reject Ho. 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 interval. Round your answers to two decimal places.) number of crashes to lie? (Use a 95% prediction

Answer 1

Let Mo = Before - After 123 51 B) 27 Betore o 16 755 84 After : ו-ד 24- רי d : 2 21 39 -18 -9 (B-A st sits) h = 6 Id=34 (Sample number d² = 2372 . The mean -a = - 15.6667 Standard deviation Sa= (ad? (Eld 2) (2372 34 Sda 2179.33333 (20.8774) (a claim: change in the mean Sd V6 number of Crashes The was any before and after the additions of distance information. ie; Moto x=0.05 level ut significance option 4 Ho: Mo=0 Ha: Moto (two-tailed test ) The test statistic tala-Mp )-(5.6667-0) 0466 (20.8714) = 10.5384 (P-value >x) Conclusion: ophon ( fail to reject to. The data does not suggest a fignificant mean difference in the average number of accidents atter information was added to road signs. The 95% predicted the difference in the number of crashes to lie dilte sa Vi+b)) = 5.6667+02:571 X20.8770x147) The 95%. Confidence interval= ((-52.31 [63-64 df=n-1=5. P-value b