Question 1 (18 points) Briefly and concisely discuss in your own words the following: 1. Definethetstatisticandthez-score.Whywouldyouchooseoneovertheother?(Giveatleasttworeasons.)(3pts) 2. CompareCohen'sdandr2.Whenandwhyaretheyused?(3pts) 3. Comparetheindependent-measuresttestwiththerepeatedmeasuresttest.Giveanexampleofeach.(3pts) 4. ExplainhowtodeterminetheFcritvalueusingTableB.4,"TheFDistribution",inAppendixBofyourtextbook.(3pts) 5. ExplainhowyoucalculatetheF-ratio,andexplainwhyitisusedinANOVA.(3pts) 6. Comparethemeansquaresbetweentreatmentswiththemeansquareswithinthetreatment.Besuretoincludetheroleof the treatment in each mean square. (3 pts) Question 2 (12 points) A random sample of n = 30 has a mean of M = 56. Test the Ho that the population mean is = 50 in situations a and b below. 1. Thesamplevarianceiss2=6:Usetwo-tailedtestat.05.Wouldthet-statisticbesignificant?Showthefivestepsof hypothesis testing. (7 pts) 2. Supposethesamplevarianceiss2=300:Usetwo-tailedtestat.05.Wouldthet-statisticbesignificant?(ShowonlySteps3 and 4 of hypothesis testing.) (3 pts) 3. Explaintheeffectofthesizeofthevarianceonthedecisionsyoumadeabove.(2pts) Question 3 (16 points) Given a sample of female students, n = 10, with SS = 600, and a sample of male students, n = 12, with SS = 700: 1. Computethepooledvariancewhenyoucombinethetwosamples.(3pts) 2. Forthecombinedsamples,whatistheestimatedstandarderrorforthesamplemeandifference?(3pts) 3. Ifyoucomputedthedifferencebetweenthemeansofthetwosamplesandobtainedadifferenceof6,isthisenoughto reject the Ho for an independent-measures hypothesis test using .01, one-tailed test? (3 pts) 4. Ifthesamplemeandifferenceyouobtainedis25points,isthisenoughtorejecttheHoforanindependent-measures hypothesis test using .01, one-tailed test? (3 pts) 5. ComputeCohen'sdtomeasuretheeffectsizeforthe6-pointdifferenceandforthe25-pointdifferenceindicatedinsub- questions c and d above. Briefly describe the effect size of each difference. (4 pts) Question 4 (13 points) A study found that lower social class people were more empathic and supportive of each other than higher social class people were among themselves. You wanted to prove this through your study on how participants from these two classes respond to a test measuring empathy and social support. Based on their scores shown in the table below, is there a significant difference on these traits between these two separate groups? Following the five steps of hypothesis testing, test at .05, two-tailed test. (NOTE: Solve SS using the computational formula.) Lower ClassHigher Class 13 10 12 10 13 17 14 13 16 12 13 11 17 13 10 10 15 12 16 16 Question 5 (17 points) After conducting your study in Question 4 above, you wanted to determine if the higher social class participants would significantly change their scores following volunteer work with a charitable organization for half a year. You re-tested them on the same test after volunteering. Was there a significant difference in their empathy and social support scores after volunteering? Using the five steps of hypothesis testing, test at .05, one-tailed test. If the difference is significant, test the effect size through r2 and describe the effect size. ParticipantAfter VolunteeringBefore Volunteering A 15 10 B 13 10 C 19 17 D 18 12 E 10 10 F 14 11 G 14 13 H 15 10 I 14 12 J 18 16 Question 6 (24 points) A psychologist found that transcendental meditation (TM) helped students perform better by increasing their GPA. He is aware that companies allowing their employees to have TM as part of their working hours became more successful. As the new industrial psychologist of a large manufacturing company, he wanted to test if it would work in the assembly unit following approval by management. He recruited 30 employees from the day shift that he divided into 3 groups: Group A didn't do TM, Group B incorporated a 15-minute TM during their lunch hour on 3 alternating days of the week, and Group C also incorporated a 15-minute TM every day of the week. The study lasted for 3 months. At the end of the study, the productivity level of the employees exceeding their required quota was noted as shown below. 1. UsingANOVA,testthesignificanceoftheapparentdifferenceinproductivitylevelat.05.(13pts) 2. Conducttwoposthoctests,Tukey'sHSDTest(5pts)andScheffeTest,bothat.05(6pts).Besuretoindicatewhichmean differences are significant in each test. Then give a conclusion comparing the results of the two post hoc tests. No TM3-day TMDaily TM 025 234 133 245 316 024 145 233 324 122