1.A sample is selected from a population with µ = 80. After a treatment is administered to the individuals, the sample mean is found to be M = 75 and the variance is s2 = 100. a. If the sample has n = 4 scores, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with alpha = 0.05 b. If the sample has n=25 scores, then calculate the estimate standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with alpha = 0.05 c. Describe how increasing the size of the sample affects he stanard erro and the likelihood of rejecting null hypothesis 2.A researcher is testing the effect of a new cold and flu medication on mental alertness. A sample of n=9 college students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each students performance is measured on a video game that requires careful attention and quick decision making. The scores for the nine students are as follows: 6,8,10,6,7,13,5,5,3. a. Assuming that scores for students in the regular population average u=10, are the data sufficient to conclude that the medication has a significant effect on mental performance? Test at the .05 level of significance. b. Compute r2, the percentage of variance explained by treatment effect. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would be presented in a research report. 3.A researcher conducts an independent-measures study examining how the brain chemical serotonin is related to aggression. One sample of rats serves as a control group and receives a placebo that does not affect normal levels of serotonin. A second sample of rats receives a drug that lowers brain levels of serotonin. Then the researcher tests the animals by recording the number of aggressive responses each of the rats display. The data are as follows. Control Low Serotonin n = 10 n = 15 M = 14 M = 19 SS = 180.5 SS = 130.0 a. Does the drug have a significant effect on aggression? Use an alpha level of .05, two tails. 4. An educational psychologist studies the effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections take the same final examination. The summarized scores below frequent quizzesn=20, M=73, two exams- n=20;M=68. a. If the sample variance is s2=38 and second has s2=42, do the data indicate that testing frequency has siggnificant effect on performance? Use a two tailed test at the .05 level of signifficance. (note because the two samples are the same size, the pooled variance is simply the average of the two sample variances.) b. If the first sample variance is s2=84 and the second sample has s2=96, to tge data indicate that testing has signifficant effect? Again use a two tailed test with Alpha=.05. c. Describe how the size of the variance effects the outcome of the hypothesis testing? 5. The following data are from an independent-measures experiment comparing two treatment conditions. treatment 1 is 4,5,12,10,10,7 and treatment 2 is 19,11,18,10,12,14. a. Do these data indicate a signifficant difference between the tretment at the 0.5 level of significance? b.wWrite a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report. 6. One of the major advantages of a repeated-measures desing is that it removes individulal differences from the variance and therefore reduces the standard error. The follwing two sets of data demonstrate this fact. The 1st set of data represents the original results from a repeated measures study. To create the 2nd set of data we started with the original scores but increased the individual differences by adding 10points to each score for subject B, adding 20 points to each score for subject C and adding 30 points to each score for subject D. Note that this change produces a huge increase in the difference from one subject to another and a huge increase in the variability of the scores within each treatment condition Set 1. Set 2. Subject I II Subject I II A 12 14 A 12 14 B 7 17 B 17 27 C 11 12 C 31 33 D 10 12 D 40 42 M=10 M=14 M=25 M=29 SS14 SS=14 SS=494 SS=414 a. Find the difference scored for each set of data and compute the mean and variance for each sample of difference scores. b. You should find that both sets of data produce the same mean difference and the same variance for the difference scores. Explain what happend to the huge individual difference that were added to the second set of data. 7. A researcher would like to examine how the chemical tryptophan, contained in foods such as turkey, can affect mental alertness. A sample of n = 9 college students is obtained and each student’s performance on a familiar video game is measured before and after eating a traditional Thanksgiving dinner including roast turkey. The average score dropped by M = 14 points after the meal with SS = 1152 for the difference scores. a. Is there is significant difference in performance before eating versus after eating? Use a two-tailed test with = .05. b. Compute r2 to measure the size of the effect. c. Write a sentence demonstrating how the outcome of the test and the measure of effect size would appear in a research report. 8. A researcher would like to determine if relaxation training will affect the number of headaches for chronic headache sufferers. For a week prior to training, each participant records the number of headaches suffered. Participants then receive relaxation training and for the week following training the number of headaches is again measured. The data are as follows: Before–After 6–4 5–1 3–3 3–1 6–2 2–1 4–3 4–2 a. Compute the mean and variance for a sample of different scores. b. DO the result indicate a significant differnce? Use a two tailed test with a=.05 9. A teacher gives a third grade class of n=16 a reading skills test at the beginning of the school year. To evaluate the changes that occur during the year, students are tested again at the end of the year. Their test scores revealed an average improvement of MD=4.7 points. a.If the variance for the difference scores is s2=144, are the results sufficient to conclude that there is significant improvement? Use a one-tailed test with a=0.05. b. If the variane for the difference score is reduced to s2=64,are the result sufficient to conclude that there is signifficant improvement? Use a two tailed test with aplha=.05 c. Describe the effect on reducing the variance of the difference score. These two 10 and 11 are short answers questions 10. Develop a unique example scenario where you as a researcher would analyze your data using an independent sample desing. 11. Alternatively, develop a unique example scenario where you would analyze your data using a related sample design. For this example scenario, pretend that you suspect you might have a attrition (or drop out) in between your data collection times. What could you do at the design phase to counteract this attrition