Question

Now that we have some familiarity with random variables, we are going to start a discussion about one of the most important random variables in statistics—the sample mean, x . Now why is x a random variable? Because its value depends on the outcome of selecting a random sample. Therefore, we can talk about its distribution, its mean or expected value, and its standard deviation. The following activity is designed to introduce the concept of the sampling distribution for x . SETUP Assume the population of Statsville has 5 residents. Each resident is asked how many times they visit the hair salon or barbershop each year. The data are shown below. 12, 13, 17, 20, 21 What is the population mean number of visits to the haircutter? What is the population standard deviation? Round to 3 decimal places. Now imagine a national chain, Clips Great, is looking to open a location in Statsville. The research team in charge of the feasibility study will want to estimate the average number of visits a resident makes each year to a haircutter. But it does not have time nor money to interview every resident. So, the team will select a simple random sample and measure the sample mean. For each sample size (n = 2, 3, 4), compute the sample mean of each sample. Next, create the probability distribution for x . Finally, use your calculator to determine the mean and the standard deviation of x based on your probability distribution. Sample (n = 2) x 12, 13 12, 17 12, 20 12, 21 13, 17 13, 20 13, 21 17, 20 17, 21 20, 21 x probability x x   = =

Answer 1