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 institute has recently signed a sponsorship deal with a shoe company. As part of the deal, the shoe company has agreed to provide a new pair of running shoes to each of the 30 5K runners. The shoe company will be shipping the new shoes in two shipments, where each shipment contains a random selection of 15 pairs of new shoes. The first shipment has arrived, so half the runners now have new running shoes. The head trainer has been notified that the second shipment has been delayed by two months. In the meantime, she would like to perform some statistical analyses using data collected fromall30 5K runners, to determine if the new shoes are better than the current shoes, in terms of improving 5K running times. Based on what we covered in the course, describe an approach that the head trainer should follow to test her claim. Make sure to clearly describe all important aspects of the approach, including the sample data needed, any hypotheses that should be tested, the test statistic(s) that should be used, the decision rule and critical value of any test(s) performed, etc. Make sure to also clearly define any parameters or sample statistics used in the approach. Assume a significance level offor any test(s) that should be performed.