Homework SourseThe Central Limit Theorem states that if I have a large numb
The Central Limit Theorem states that if I have a large number of samples from a population, the means of the samples will form a normal distribution, no matter what the distribution of the original population is. Why is this important?
It allows us to generalize from a sample to a population
It means that all distributions are really normal distributions.
It proves that all samples are good indicators of the population.
It means that researchers can reliably generalize from even very small samples to the full population.
| 1. | It allows us to generalize from a sample to a population | |
| 2. | It means that all distributions are really normal distributions. | |
| 3. | It proves that all samples are good indicators of the population. | |
| 4. | It means that researchers can reliably generalize from even very small samples to the full population. |
Solution
ACtually all 4 are wrong. The actual reason is that we can easily construct CI or hypothesis if sample mean follows normal distribution. Both Z and T are based on normality. Even comparison of means and comparison of variances requires sample mean to be normal. This is not related to small samples sizes because a larger sample size has better approximation to normal distribution for sample mean.
