A technology start-up company has had 5 different CEOs since it was founded. The tenures of these CEOs - the number of months that they held the position - are given in the table below. These 5 CEOs are the population you are interested in.

CEOTenure (in months)

112

214

36

419

512

You randomly select a sample of 2 CEOs from the population. The sample you get is (CEO3, CEO4). Based on this sample, what is your point estimate of the population mean of tenure?

Calculate the sampling error of the point estimate you found in question 1. Are you underestimating or overestimating the population mean?

Suppose that you randomly sample 2 CEOs without replacement. In the table below, list all possible samples you could select and the value of the sample mean of tenure () in each sample.

Sample

Under simple random sampling, what is the probability of each sample you wrote down in question 3?

For each CEO, calculate the probability that he/she is selected into a sample. Comment on your answer.

Use your answers to questions 3 and 4 to write down the probability distribution of the sample mean(i.e. a table with possible outcomes and associated probabilities).

Calculate the expected value of . How does your answer compare to the population mean of tenure?

Suppose that you sampled 2 CEOs with replacement instead. How many different samples are possible, and what is the probability of each sample occurring?