Pencil and Paper Exercises on Sampling Statistics 1. The scores of individual students on the American College Testing Program (ACT), a university admission exam, follow the normal distribution with mean of 18.6 and a standard deviation of 5.9 At one school 81 students participated in the test. Determine the expected mean (sample mean) and standard deviation (standard error) of groups of 81 students. 2. The scores of individual students on the American College Testing Program (ACT), a university admission exam, follow the normal distribution with mean of 18.6 and a standard deviation of 5.9 (a) What is the chance that a randomly selected student scores 21 points or higher? (b) The class average of one class of 81 students was m=20.4 What is the chance that the average of a randomly chosen group of 81 students would be 20.4 or higher. 3. In one experiment on reading ability two techniques are compared, A and B. The variable to be predicted is the reading score known as 'Degree of Reading Power'(DRP). The researcher used method A in a group of 25 pupils and method B in a second group of 16 pupils. Pupils were randomly assigned to one or the other group. Assume that the population of all children of the relevant age follows a N(34,10) distribution in the case of method A, and a N(37,12) distribution in the case of method B. (a) What is distribution of the average DRP scores for method A in groups of 25 pupils? Assume that these group may be viewed as randomly selected samples. (b) What is the distribution of average scores for method B in groups of 16 pupils.