Conceptual Stuff about Sampling Distributions

Here are a few key stats-y points about sampling distributions that you want to keep in mind, especially when you are doing your problem set (10 bonus points if you recommend me a good workout song at the end of your problem set!).

1. If your z-score is positive, then your x-bar should be greater than your mu. If your z-score is negative, then your x-bar should be lower than the mu. If they are the same, then the z-score should be zero and your probability will be 50%.

2. When n is low, the z-score becomes smaller. When n is higher, the z-score becomes larger (if all other variables are held constant).

3. Your z-score represents how many standard deviations your sample mean is from your population mean. If the z-score is within + or - 3 standard deviations from the mean, then we can assume that the sample is representative of the population without calculating the probability. If the z-score is more than -3 or +3 standard deviations from the mean, then are sample mean is too far from the population mean to say that the sample accurately represents the population.

4. If a problem asks you to find the probability that the sample is "between" two different sample means, find the probability of the first (Normalcdf(first z-score)), then find the probability of the second (Normalcdf(second z-score)), then subtract those probabilities.

Remember that a probability MUST be between zero and one - ALWAYS!!!