In the 2016 Rio Olympics, the 207 participating countries had an average of 54.3 athletes. After being delayed a year because of Covid-19, the Tokyo Olympics were held in July and August 2021. Because of ongoing issues with the pandemic, no fans were allowed at the events. A random sample of 37 countries participating in the Tokyo Olympics had an average of 51.3 athletes, with a standard deviation of 112.8. Estimate the mean number of athletes per country participating in the Tokyo Olympics with 98% confidence.

1. At a 95% level of confidence, what sample size would be needed to estimate the parameter of interest to within a margin of error of 20 athletes? Use = 110 athletes. Show your work and correct formula.

2. Interpret your confidence interval in context. Do this by including these three parts in your conclusion : Level of confidence Parameter of interest in context The interval estimates