I have sampled from two separate populations, and I want to figure out which population is better.
Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an average score of 95.8 and a standard deviation of 13.5.
Assume that all samples are independent, and the sample size is 500 for each population.
What is the best way to prove that a random sample from population 2 will result in a greater score (on average) than a random sample from population 1?
What statistic do I need? Confidence interval? Tolerance interval?