Part 3a) For each the following questions, calculate the standard error of the mean (SEM) or the standard deviation of the distribution of means from the variance of the population OR from the standard deviation of the population (refer to the two different formulas given in class depending on whether you are working with the variance or standard deviation of the population. Once you've calculated the SEM, draw a curve and plot the mean and 2 standard deviations (SD) above and below the mean (plot the SDs in raw scores values as shown in the example). After calculating the first two answers you'll see that by increasing sample size, the SDs around the second mean get smaller because the sample size is larger. In other words, if we were to sample another mean from the distribution again (given the same sample size) it should be closer to the actual population mean that it was sampled from, on average. Why? It has more people from the population in it (so the deviations or sampling error is smaller). In the first example, the SDs are larger, so if we sampled another mean again (given the same smaller sample size) the mean would differ more from the population mean, on average.

EXAMPLE Mear Variance Sample Size (N) 100 900 50 O =900/50 =18 = V18 =4.24 91.52 95.76 100 104.24 108.48 Mean Variance Sample Size (N) 50 225 25 OM Mean Standard Sample Size (N) Deviation 50 15 100 OM =Study Mean () Standard Sample Sample Alpha (a) Tails of Deviation (o) Mean Size (N) Test A 100 15 104 20 05 2 Study Mean (H) Standard Sample Sample Alpha (Q) Tails of Deviation (o) Mean Size (N) Test B 100 15 104 72 05 2 (Notice you get different answers in A and B. This reflects what happens when your sample mean differs from the population mean and you sample more participants) Study Mean (H) Variance (o') Sample Sample Alpha (@) Tails of Mean Size (N) Test C 100 225 95 65 01 1 (low)