Question

1. List all possible samples of n=2 from the following population {1,2,3,5,6,7} (note that there is no number 4 in the population). Assume that those numbers represent the years of age of six different people. Create a sampling distribution of the 15 different sample means based on each possible pair (e.g., the sample {2,1} represents on possible such pair). Assume further that the order of the numbers does not matter (e.g., the pair {1,2} is the same as the pair {2,1}). Compute the expected value of the resulting sampling distribution (i.e., the mean age or μ) based on the 15 different sample means. Compute the standard deviation (i.e., the standard error or SE) of the resulting sampling distribution based on the 15 different sample means.

2. Based on the sampling distribution you created in question 2 above, what is the probability of underestimating (i.e., the probability to the left) the true population mean age (μ) by 2 years.

Answer 1