Rounding policy:

• Proportion: 4 decimal places
• Percentile: round to the closest whole unit number
• All others: 2 decimal places

1. Briefly define each of the following: a. The distribution of sample means b. The expected value of M. c. The standard error of M 2. Describe the distribution of sample means (shape, mean, and standard error) for samples of n = 64 selected from a population with mean of ,u = 136 and a standard deviation of a = 24. 3. Two samples are randomly selected from a population. One sample has n = 5 and the second has n = 30. Which sample should have a mean (M) that is closer to ,u? Explain your answer. 4. A local high school counselor is interested in studying how teacher perceptions of students, as being intelligent or not, affect the success of freshman students in the classroom. The school creates an Excel spreadsheet listed all the freshman students in alphabetical order and places their names into one of two columns. All students listed in the second column are selected to participate in this study. Is this design an example of random sampling? Explain 5. A distribution of final exam scores is normal, with ,u = 500 and a = 100. a. If you selected a random sample of n = 4 scores from this population, how much error would you expect between the sample mean and the population mean? b. If you selected a random sample n = 25 scores, how much error would you expect between the sample mean and the population mean? c. How much error would you expect for a sample of n = 100 scores? d. What do we notice about the standard error as the sample size increases? 6. Can the standard error ever be larger than the population standard deviation? Explain your