Download Random Sampling: Obtaining and Exploring Sample Means in Minitab - Prof. Edith Seier and more Lab Reports Statistics in PDF only on Docsity! LAB on Random Samples 1. How to obtain a random sample from a population using Minitab Assume that you want to select a random sample of size 50 from a population of size 4000. The sampling frame The first thing you need to do is to prepare the sampling frame. That means that you need to have a list of all the members of your population and number them from 1 to 4000, i.e. we need to assign a numerical label to each element of the population. Preparing the labels with Minitab We will create a list of numbers from 1 to 4000. To do that use CALC>MAKE PATTERNED DATA>SIMPLE SET OF NUMBERS Indicate that you want to store the numbers in C1 starting from 1 and ending with 4000 in steps of 1. Type the name of C1 : LABELS Selecting a simple random sample. From the menu, select CALC>RANDOM DATA>SAMPLE FROM COLUMNS indicate that you want to select a sample of size 50 from column C1 and store the sample in C2. Now in C2 you have the labels of the 50 people that are in the sample. These individuals are the ones that will be interviewed in a hypothetical survey. 2. Exploring the idea of sampling variability Open the data file agepop.mtw. The data file contains the ages for a real population of 4000 people (18 years or older). Hence, we know the true mean value of the variable age for the whole population. This is a special situation that is not usually the case in surveys. The values in C1 are not the labels, they are the values of the variable age. Obtain a histogram and calculate the mean for the values in C1. μ = _________ Report also the minimum ________ and the maximum ______values. a) Take a simple random sample of size 40 from column C1 and place it in C2. b) Take another simple random sample of size 40 from column C1 and place it in C3. c) Take another simple random sample of size 40 from column C1 and place it in C4. Use STAT>Basic Statistics to calculate the sample mean for each one of the 3 samples (you can do this calculation all at once by using the descriptive statistics on the columns C2-C4). 2.1. Report the sample means (average age in the sample) for each one of the samples of size 40 (Note that your values will differ from each other because they are different random samples) Sample 1 x _____________ Sample 2 x _____________ Sample 3 x ______________ 2.2. Are the 3 sample means equal? YES NO (We call this “sampling variability.”) 2.3. Are the sample means exactly equal to the population mean? YES NO 2.4. On the axis below, mark with an X the population mean and with dots the sample means _________________________________________________________________ 20 30 40 50 60 70 80 90 3. Exploring the idea of sampling distribution In part 2 you randomly selected 3 samples, calculated the sample means and observed how they were around the population mean. Now think about not just 3 possible samples but of all the possible samples of size 40 that you could take from that population. How would the values of the sample mean be distributed? Would they be around the population mean?
