Question 1169004: NHTSA new car crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data on new cars, saved in the CRASH file. Crash test dummies were placed in the driver’s seat and front passenger’s seat of a new car model, and the car was steered by
remote control into a head-on collision with a fixed barrier while traveling at 35 miles per hour. Two of the variables measured for each of the 98 new cars in the data set are (1) the severity of the driver’s chest injury and (2) the severity of the passenger’s chest injury. (The more points assigned to the chest injury rating, the more severe the injury is.) The files demonstrated that the mean chest injury rating was significantly higher for drivers than for passengers. A similar study utilized independent random samples of size 18 and yielded the data shown in the table below on the chest injury rating of cars for drivers and passengers.
Chest Injury Rating
Car Driver Passenger Car Driver Passenger
1 42 35 10 36 37
2 42 35 11 36 37
3 34 45 12 43 58
4 34 45 13 40 42
5 45 45 14 43 58
6 40 42 15 37 41
7 42 46 16 37 41
8 43 58 17 44 57
9 45 43 18 42 42
Question: State the null and alternative hypotheses.
Thank you!
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! To state the null and alternative hypotheses for this study, we need to define the population parameters we are comparing.
Let:
* $\mu_D$ = the population mean chest injury rating for drivers
* $\mu_P$ = the population mean chest injury rating for passengers
The previous study found that the mean chest injury rating was significantly higher for drivers than for passengers. We want to test if this finding is supported by the data in the table.
Here's how to state the null and alternative hypotheses:
* **Null Hypothesis ($H_0$):** The null hypothesis generally states that there is no difference or no effect. In this case, it would be that the mean chest injury rating for drivers is less than or equal to the mean chest injury rating for passengers.
$H_0: \mu_D \le \mu_P$
* **Alternative Hypothesis ($H_a$):** The alternative hypothesis states what the researcher is trying to find evidence for. In this case, it would be that the mean chest injury rating for drivers is greater than the mean chest injury rating for passengers, consistent with the previous study's finding.
$H_a: \mu_D > \mu_P$
In summary:
* **Null Hypothesis ($H_0$):** $\mu_D \le \mu_P$
* **Alternative Hypothesis ($H_a$):** $\mu_D > \mu_P$
This is a one-tailed (right-tailed) test because we are specifically looking to see if the driver's injury rating is *greater* than the passenger's.
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