Final answer:
The question involves applying statistical methods to examine if there's a correlation between the brand option (d) of running shoes and runners' performance in a marathon.
Step-by-step explanation:
The question pertains to the field of statistics, which falls under mathematics. A marathon runner records the run times and brand of shoes worn by a random sample of 50 runners. This study aims to analyze the correlation, if any, between the runners' performance and their shoe brand choice.
The statistical method for such analysis could involve calculating correlation coefficients, performing a regression analysis, or using analysis of variance (ANOVA) if comparing multiple brands. By scrutinizing the collected data, the marathon runner seeks to understand whether a particular brand contributes to faster run times, or if the differences are statistically insignificant.