Kirstyn conducted an experiment to determine if high school athletes run faster after warming up. She randomly selected 30- athletes from her large school and had them run a 100-meter sprint with and without warming up (one week apart), randoml determining which they ran first. For each runner, she calculated the difference (No warm-up- Warm-up) in 100-meter sprim times, in seconds. The mean of the differences is an = 1.293 seconds and the standard deviation is sar 0.438 seconds. (a) Why should you use paired t procedures to perform inference about a mean difference in this setting? The subjects were randomly assigned to treatment groups. O The experiment used a control group. There was a random sample of athletes. The data come from a matched pairs experiment with the order of the two treatments being randomly assigned to each athlete. (b) Is there convincing evidence at the a=0.05 significance level that athletes from this school run faster (have shorter times), on average, when they warm up? STATE: Ho H where athletes like these. Use a =0.05. 0 0 the true mean difference (No warm-up- Warm-up) in 100-meter sprint times (seconds) for The evidence for Ha is: -1.293 0.