A track-and-eld coach would like to know how the 100-metre sprint-times of the athletes within a sizeable region compare to the national team's mean 100metre sprint time of 12.21 seconds. The coach randomly draws 10 sprinters out of the regional sprinters, and nds their mean 100-metre sprint time to be 11.83 seconds, with a sample standard deviation of 0.55 seconds. a. State an appropriate statistical test for the coach to conduct to answer his research question, and state the null and alternative hypotheses of the test. [2 marks] b. Conduct the appropriate statistical test by hand calculation, using an alpha value of 5% as the signicance criterion. What are the results of this statistical test, and what should the coach conclude based on the results? [5 marks] c. From looking through the records of all the regional athletes later on, the coach nds that their standard deviation is 0.62 seconds. Using this piece of information along with the available information so far, calculate the 95% condence interval of the regional athletes' mean 100-metre sprint times. [5 marks]