You are sampling one observation at a time from this population (n=1), what does the sampling distribution look like? Define the sample space, and the probabilities of the relevant events. Create a graph of this sampling distribution. Calculate the expected value, variance, and standard deviation for this sampling distribution. What is the probability that your observation has a value of 5 or more? (Not knowing what your population looks like, this may not be a reasonable number to work with. If it isn’t, then pick some other number that is.)
Now consider that you are sampling two observations at a time, with replacement (n=2). You take the mean of those two observations. Define the sample space, and the probabilities of the relevant events. Create a graph of this sampling distribution. Calculate the expected value, variance, and standard deviation for this sampling distribution. In what ways is this distribution similar to or different from the distribution of scores in the population, or the sampling distribution when n=1? What is the probability that your sample will have a mean of 5 or more?
Create for yourself a small population (N less than 20). This time, however, the population contains observations that can only take one or the other of two possible values. (For simplicity, use values of 0 and 1.) Also, avoid making all of the population ‘0’s or ‘1’s. With this as your population, create the ordered array and from there the frequency distribution table.
Now consider that you are sampling two observations at a time, with replacement (n=2). You take the mean of those two observations. Define the sample space, and the probabilities of the relevant events. Create a graph of this sampling distribution. Calculate the expected value, variance, and standard deviation for this sampling distribution. In what ways is this distribution similar to or different from the distribution of scores in the population, or the sampling distribution when n=1? What is the probability that your sample will have a mean of .5 or more?
Now consider that you are sampling 100 observations at a time, with replacement, and take the mean of these 100 observations. What would the sampling distribution look like in this case? What would be the mean, variance, standard deviation, and shape of this distribution? What is the probability that your sample will have a mean of .5 or more?
Now, take a sample of size 4 from your population, with replacement. Make sure that it is a probability sample. Review the techniques for selecting a simple random sample from Chapter 1. Now that you have a sample of 4 observations, what are the mean, variance, and standard deviation of this distribution? Create a graph for this distribution. Now how does this distribution compare to the original population? How does it compare to the sampling distribution?
Consider that you would take another sample of size 4, and another, and so on; each time recording the mean of the sample. If you did this 100 times, or 1000 times, what would the resulting distribution of means look like?