Question

One recent research with 863 people randomly selected from LA county suggest that 3.5% of its 10.4 million residents had been infected by COVID-19. One condition for central limit theorem is not satisfied here, because the sample size 863 is too small comparing to the total population 10.4 million. True or false?

Answer 1

False, because when applying Central Limit theorem for normal approximation, we look for random sample and another assumption is that number of success and failure(in terms of Bernoulii trials) i.e, number of persons with disease and without disease should be greater than 10 and with disease should also be greater than 10 alnong with sample size being greater than 30,

Here, n is larger than 30, and persons with disease is 3.5% of 863 = 30.205 hence all assumptions are satisfied.