At an athletics institute, there are currently 30 athletes who specialise in the 5000 metre run (5K run). The institute is world-renowned for its training programs that produce very consistently performing athletes. As such, the 30 5K runners are all considered to have similar running ability. Further, a runner's performance when running a 5K race is independent from runner to runner.

The head trainer at the institute recently read an article in a sports science journal about optimal body mass index (BMI) for long distance runners, which has inspired her to perform some data analyses herself. She measured the BMI of each of the 30 5K runners, and the sum of the BMI values was 614.4 and the sum of the squared BMI values was 12591.4264. Based on these sample data, test whether the mean BMI of 5K runners who have trained at the institute is less than 20.8. Clearly state your hypotheses and use a significance level of.