A research team is working on a project to study the time (in seconds) for high school male runners to finish a 400-meter race. Jimmy, a junior researcher in the team, has randomly selected a sample...

Extracted text: A research team is working on a project to study the time (in seconds) for high school male runners to finish a 400-meter race. Jimmy, a junior researcher in the team, has randomly selected a sample of 25 male runners from a high school and the time (in seconds) for each of them to complete a 400-meter race was recorded. The sample mean running time was 53 seconds. It is assumed that the running time in a 400-meter race follows a normal distribution with a population standard deviation of 5.5 seconds. (a) Give a point estimate of the population mean running time for a 400-meter race. (b) Calculate the sampling error at 95% confidence level. (c) Construct a 95% confidence interval estimate of the population mean running time for a 400-meter race. (d) If instead of 25, 80 male runners are selected for the study, what is the sampling error at 95% confidence level? When the 95% confidence interval is constructed based on a sample with 80 male runners, would you expect the interval will be (I) narrower, (II) wider, or (III) the same width as the confidence interval constructed in part (c)? (e) After discussion with the research director, Jimmy is asked to work on the research again. This time, he needs to ensure the difference between the point estimate and the true population mean be within + 0.8 seconds at 99% confidence level. To fulfil the requirement, how large should be the minimum sample size?