A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one-way commute time of 38 minutes with a standard deviation of 8 minutes. Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 30 minutes? \[ H_{0}: \mu=30 ; H_{A}: x=38 \] \( H_{0}: x=38 ; H_{A}: \mu=30 \) \( H_{0}: \mu=30 ; H_{A}: \mu \neq 30 \) \( H_{0}: \mu=30 ; H_{A}: \mu>30 \) Ouestion Help:

In hypothesis testing, you're trying to determine if there's enough evidence to support a change from the status quo. In this case, you want to test if the average commute time differs from the established norm of 30 minutes. If we look at the options, the correct hypothesis set should indicate that you are testing for any difference, not simply one direction (greater or less). Here, the null hypothesis \( H_{0} \) assumes no difference, while the alternative hypothesis \( H_{A} \) reflects the possibility of a difference—either greater or less than the standard. So, the accurate formulation for this scenario is: \( H_{0}: \mu=30 ; H_{A}: \mu \neq 30 \). This means you are checking to see if the average commute time actually differs from 30 minutes, regardless of the direction. When conducting hypothesis tests, keep in mind that the significance level (usually set at 0.05) will dictate how much evidence you need against the null hypothesis to conclude that your sample data shows a significant effect. If you determine that the average time does differ significantly from 30 minutes, it can pave the way for reassessing transportation policies and improving student commute experiences!