Rounding policy:

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

Briefly define each of the following: a. The distribution of sample means b. The expected value of M. c. The standard error of M Describe the distribution of sample means (shape, mean, and standard error) for samples of n = 64 selected from a population with mean ofu = 136 and a standard deviation of a = 24. 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. 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 A distribution of final exam scores is normal, with y = 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? 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? 9 6. Can the standard error ever be larger than the population standard deviation? Explain your answer. 7. A population has [A = 60 and a = 10. Find the z-score corresponding to each of the following sample means: a. A sample of n = 4 with M = 55 b. A sample of n = 25 with M = 55 c. A sample of n = 100 with M = 55 cl. What do we notice about the z-scores as the sample size changes 8. If you are taking a random sample from a normal population with u = 100 and a = 16, which of the following outcomes is more likely? Explain your answer. a. A sample mean greater than 106 for a sample of n = 4. b. A sample mean greater than 103 for a sample of n = 36. 9. A sample of n = 26 scores is selected from a normally distributed population. State whether the standard error will increase or decrease if the sample size is changed to: a. b. c. d n=3& n=5 n=28 n=25 10. A researcher evaluated the effectiveness of relaxation training in reducing anxiety. One sample of anxiety ridden people received relaxation training, while a second sample did not. Then anxiety scores were measured for all subjects, using a standardized test. Use the information summarized in the following table to complete this item. a. b c. d. e f. g h The Effect of Relaxation Training on Anxiety Scores Group Mean Anxiety Score SE Control group 36 7 Relaxation 18 5 training What is the independent variable (IV)? How many levels do we have for the IV? What is the level of measurement for the IV? What is the DV (remember, the DV is the data)? . What is the level of measurement of the DV? What is the best graph to display this data? Explain Construct a graph (by hand) that incorporates all the information in this table. Looking at your graph, do you think that the relaxation training really worked. Explain your answer. 11. A researcher assessed the effects of a new drug on migraine headaches. One sample of migraine sufferers received a placebo pill (0 milligrams of the drug) every day for a month. A second sample received a 10-mg dose of the drug daily for a month, and a third sample received daily doses of 20-mg. The number of headaches each person had during the month was recorded. The results are summarized in the following table: The Mean Number of Migraines During Drug Treatsment Dose of Drug Mean Number of Migraines a. What is the independent variable (IV)? How many levels do we have for the IV? What is the level of measurement for the IV? What is the DV (remember, the DV is the data}? What is the level of measurement of the DV? What is the best graph to display this data? Explain. Construct a graph (by hand} that incorporates all the information in this table. Looking at your graph, do you think that the new drug treatment really worked. Explain your answer. ?QT\"PPPP' 12. A recently admitted class of graduate students at a large state university has a mean GRE verbal score of 650 with a standard deviation of a = 50. The scores are normally distributed. One student, whose mother just happens to be on the board of trustees, was admitted with a GRE score of 490. Should we be concerned about favoritism? 13. Use the table below to answer items (a) (e). The Procrastination Log (PL)...was administered both at intake [pretest to a one-hour individual counseling session on procrastination] and on outtake [posttest]. The PL is the most widely used instrument for assessing difficulties with procrastination. It is a 9- item self-report questionnaire that measures procrastination-related behavior during the past week. Group Means and Standard Deviations of Procrastination Log scores Intake Outtake Group M SD M SD Same-attribution group (n = 27} 43.5 8.6 37.4 9.1 No attribution group (n = 27) 45.7 5.9 33.4 10.8 Different-attribution group (n = 27) 41.9 10.7 36.8 9.2 *Higher scores indicate greater self-reported procrastination 9' On average, which group had the higher scores on \"Intake'? b. At \"Intake" which group has the greatest variability in their scores? c. On average, which group showed the greatest improvement from \"lnta ke\" to "Outtake"? d. Assuming that the distribution of PL scores for the "No attribution group" at "Intake" is normal, between what two scores did approximately the middle 95% of participants lie? e. Assuming that the distribution of PL scores for the "No attribution group" at "Outtake" is normal, between what two scores did approximately the middle 99.7% of participants lie