Final answer:
The purpose of the testing is selection for a competition. The new stopwatch is effective despite its ±0.05 s uncertainty, as it can still distinguish sprinters close to the 12-second cutoff. It can also verify improved performance across different weeks.
Step-by-step explanation:
The purpose of testing reflected in the scenario where a physical education teacher tests her students in the 100-yard dash and only submits the names of those who run under 12 seconds is to select athletes for a university track and field competition. This is an example of selection testing, which aims to choose individuals based on their performance, in this case, their speed in the 100-yard dash.
In terms of the coach's new stopwatch with an uncertainty of ±0.05 s, this tool would be helpful for timing the sprint team because the difference between the first and second-place sprinters is 0.03 seconds, which is within the uncertainty range of the stopwatch.
Therefore, when considering the selection for the university competition, the new stopwatch can still be considered accurate enough for the purpose of determining which athletes are under the 12-second cutoff.
Finally, when comparing the times of the team's top sprinter from one week to the next, where they clocked 12.04 seconds and 11.96 seconds respectively, we can conclude that this week's time was faster. However, considering the uncertainty of ±0.05 seconds, we should note that the actual times might slightly differ, but given the difference is larger than the uncertainty, the conclusion remains valid.