Exam 2 PS 306, Fall 20011. Suppose that you are interested in learning which factors lead to better performance on exams.Thus, you decide to use test performance (% correct) as your dependent variable. You will havea group of participants study in preparation for a test in an obscure area of knowledge for thetypical person (that is, a topic about which people are unlikely to know a lot of information).[Why would you want an obscure content area for your experiment?] You decide that you wantto use two independent variables: number of hours spent studying and the extent to which thematerial being learned is inherently interesting. Prior to beginning the study, you have anindependent group of students rate the extent to which 10 topics are interesting. From the 10topics, you choose 3 to use in your study (the topic rated least interesting, the topic rated mostinteresting, and a topic rated in the middle in terms of interest). Thus, the Interest factor has 3levels, which I would like you to treat as a repeated measures factor. The number of hours spentstudying that you assess is up to you, except that the factor must contain at least 3 levels and itmust be an independent groups (between groups) factor. Therefore, the experiment you are aboutto design is at least a 3x3 mixed design (though it could have more than 3 levels of the HoursStudying factor if you so choose). Think carefully. What I want you to do is to lay out for me infairly explicit detail how you would design/conduct this experiment. Be sure to address all theissues that we have discussed that would be important in designing experiments of this sort. Iwant you to provide sufficient detail so that I can tell that you’ve thought through the experimentin concrete terms. Be explicit!! [25 pts]You would want obscure content areas to minimize the possibility that participants willcome to the experiment with prior knowledge of the topic. After the selection process (from10 possibilities) you would choose 3 content areas of Low, Medium, and High Interest.Because you’re treating interest as a repeated variable, you would need to counterbalancethe order in which the three content areas are studied. With only 3 levels, completecounterbalancing would make the most sense, so you would need 6 orders (LMH, LHM,MLH, MHL, HLM, HML). If the person studies all 3 at one sitting, you’d have to becareful to keep the maximum amount of study time reasonable (e.g., less than .5 hour pertopic). If you decided to spread the study time over three separate days, you could uselonger study times, but you should recognize that you might run into attrition problems.Even with the use of presumably obscure topics, of course, you would need to include a 0hours study condition as a control for prior knowledge.So, one possible set of study times might be 0, .5, and 1 hour (if you conducted the studyover a few days). That is, one group would study L from .5 hour on Day1, M for .5 hour onDay2, and H for .5 hours on Day3 (with 5 other groups getting the other 5 orders). Ofcourse, one group wouldn’t study at all, but would just take the test. (Although you mightconsider bringing them to the lab for some time to study something different, to ensure thattheir performance isn’t adversely affected just by being uncomfortable in the lab.) Toachieve sufficient power, I might shoot for 30 pieces of data in each condition, so I’d needto run a total of 90 participants (30 in the 0 hour, 30 in the .5 hour, and 30 in the 1 hourstudy conditions).2. Most adolescents experience a growth spurt when they are between 12 and 15 years old. Apsychologist studying the physical development of adolescents recorded the gain in height (incentimeters) over a 1-year period for boys and girls ranging in age from 11 to 15. Thus, the Agefactor has 5 levels. The other factor of interest is Gender. The partially completed source tablefor this 2x5 design is seen below. Complete the source table and then interpret the study ascompletely as you can. [20 pts]4 38.067 9.517 10.160 <.0001 40.641 1.0001 18.150 18.150 19.377 <.0001 19.377 .9964 191.933 47.983 51.228 <.0001 204.911 1.00050 46.833 .937DF Sum of Squares Mean Square F-Value P-Value Lambda PowerAgeGenderAge * GenderResidualANOVA Table for Growth6 5.833 .753 .3076 4.833 .753 .3076 8.500 1.049 .4286 4.833 .983 .4016 6.167 .753 .3076 5.833 1.169 .4776 3.667 .816 .3336 8.500 1.378 .5636 1.500 .548 .2246 7.167 1.169 .477Count Mean Std. Dev. Std. Err.11, Female11, Male12, Female12, Male13, Female13, Male14, Female14, Male15, Female15, MaleMeans Table for GrowthEffect: Age * GenderBecause the interaction is significant, that’s where you should focus your attention.123456789Cell Mean11 12 13 14 15CellMaleFemaleInteraction Line Plot for GrowthEffect: Age * GenderA graph of the data helps clarify the nature of theinteraction. To determine which specific means differed, you would need to compute HSD.† HSD = qMSErrorn= 4.69.9376= 1.85 Thus, at Age 11 and at Age 13, Males and Femaleshave equivalent growth rates. However, at Age 12 Females have a significantly largergrowth rate than Males. Furthermore, at Ages 14 and 15, Males have significantly largergrowth rates than Females.3. A researcher interested in group dynamics hypothesizes that when groups of people are givena problem to solve, they will reach a unanimous consensus more quickly if the group iscomposed of members of the same gender than if the group is composed of people of bothgenders. She proposes the following independent groups design (3 levels): a group of 6 males, agroup of 6 females, or a group of 6 males and 6 females will meet in a conference room. (Thus,there are three different types of groups defined by gender composition.) The researcher willgive the participants biographies of three people who are being considered for an advisoryposition in a shipping company. The group's task is to select one of the applicants for theposition through discussion and deliberation. The experimenter will be present to act as amoderator, but she will not attempt to sway the decision in one way or another. The amount oftime needed to reach a decision will be the dependent variable. Are there any problems with thisprocedure? [10 pts]You should notice right away that the group sizes differ (as well as the group composition).Thus, one way to fix that problem would be to have 12 females, 12 males, and a group of 6males and 6 females. You should also notice that the