Another seat belt scenario. A study of seat belt use involved children who were

Question

Another seat belt scenario. A study of seat belt use involved children who were hospitalized as a result of motor vehicle crashes. For a group of 300 children who were not wearing seat belts, the number of days spent in intensive care units (ICU) has a mean of 1.50 and a standard deviation of 3.06. For a group of 130 children who were wearing seat belts, the number of days in ICU has a mean of 0.96 and a standard deviation of 1.77 (based on data from "Morbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts" by Osberg and Di Scala, American Journal of Public Health.) At the 0.025 significance level, test the claim that the population of children not wearing seat belts has a higher mean number of days spent in ICU. Based on the result, is there significant evidence in favor of seat belt use among children.

Explanation / Answer

Null Hypothesis : H0: there is no difference in between day spent in ICUs for Children who wear seat belts and who don't. Beltwear = dontwear belt

Alternative Hypothesis: Ha : There is significant evidence that mean day spent in ICUs for Children are lesser than who don't wear seat belt. Belt wear < dont wear belt

Test Statistic :

xnobelt wear = 1.50 ; snobelt wear = 3.06 and n1 = 300

xbelt wear = 0.96 , sbeltwear = 1.77 and n2 = 130

Z = (xbelt wear - xnobelt wear) / sqrt [ s2nobelt wear / n1+ s2beltwear/n2]

Z = ( 0.96 - 1.50) / sqrt [ 3.062/ 300 + 1.772/ 130]

Z = -0.54/ 0.2352 = -2.295

at one directional alpha = 0.025 significant level Z value = 1.96

so Z > Zcriticalso we can reject the null hypothesis and claim the evidence that mean day spent in ICUs for Children are lesser than who don't wear seat belt.

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