Smith and Wells (2006) conducted a simulation study to analyse sampling distributions of the mean from realistic non-normal distributions for a range of sample sizes in order to determine when the distribution of the sample mean is approximately normal.
statistics
Description
Part a.
Smith and Wells (2006) conducted a simulation study to analyse sampling distributions of the mean from realistic non-normal distributions for a range of sample sizes in order to determine when the distribution of the sample mean is approximately normal. Their findings suggest that as the skewness and kurtosis of a distribution increase, the Central Limit Theorem (CLT) will need sample sizes of up to 300 to provide accurate inference. By generating different random samples n = 50, 100,200,400, 1000 from Gamma (or Beta) distributions with skewness and kurtosis greater than 2, show that their findings are true.
Part b. The Men’s decathlon competition at the Summer Olympic Games Rio 2016 in Rio de Janeiro, Brazil, was held 17 August to 19 August 2016. It is usually held over two days. The decathlon consists of ten track and field events, with a points system that awards higher scores for better results in each of the ten components. The athletes all compete in one competition with no elimination rounds. The track events are 100 metres, 400 metres, 110 metres Hurdles and 1500 metres. The field events were Long Jump, Shot Put, High Jump, Discus Throw, Pole Vault and Javelin Throw. The decathlon always starts and ends with a running event. The file Decatholon 20l6Rio.csv contains the above data. Do the principal component analysis on the raw data.
