Consider a population of five items identical in appearance but weighing 9, 13, 15, 17, and 19 grams.
1. Determine the mean and the variance of the population.
2. How many possible samples can we have if we sample without replacement from the above population with a sample size of 2. Please justify your choice of counting rule to determine the number of possible samples.
3. Write down all the possible samples, either in a linear format (i.e. a simple list) or using a tree diagram.
4. Using the ten sample-mean values, estimate the mean of the population and the variance of x .
5. Compute the standard error of the mean.
6. What is the relevant theorem that describes the behaviour of the sample mean when repeated samples are taken? Briefly describe the theorem in your own words.