Exam 1 PS 306, Fall 20021. Searching for the dangers of caffeine, Dr. Hy Test adds two types of caffeine (those found in coffee andchocolate) to the water supply of groups of laboratory-bred rats. The water supply of a control group of rats was notfortified. This species ordinarily lives about 13 months. The DV is the number of days that the rats lived. Completethe analysis below, interpret the results as completely as you can, and then tell me very specifically what you woulddo next. [10 pts.]2 33.250 16.625 .084 .9194 .169 .06121 4136.375 196.970DF Sum of Squares Mean Square F-Value P-Value Lambda PowerCaffeineResidualANOVA Table for Days Lived8 397.750 14.140 4.9998 400.500 16.009 5.6608 399.875 11.606 4.103Count Mean Std. Dev. Std. Err.ChocolateCoffeeNoneMeans Table for Days LivedEffect: CaffeineBecause the F-value is small (and the P-Value > .05) you would retain H0. Thus, it seemsreasonable to conclude that on the basis of this particular study, caffeine (in the formsadministered) did not have an impact on the longevity of the rats.Next, of course, you'd need to think about issues of power. How could you make this studymore powerful? The most obvious approach would be to increase sample size from 8 tosome greater number (30? 50?). You should also consider the treatment level. Could theamount of caffeine added to the water supply be increased? You should also consider howyou might decrease MSError. One possibility would be to make the rats more similar (littermates?). Another possibility would be to make sure that the environments of the rats wereas close to identical as possible (so that exercise opportunities, type and amount of foodprovided, etc. were the same).2. An interesting psychological trait is openness to experience: a willingness to try new things and to keep an openmind (McCrae, 1996). Another often researched trait is authoritarianism: a general belief that society is better offwith strongly enforced laws and punitive parents and bosses to keep people in line. To determine if the two traits arerelated, a randomly selected group of students was given both scales. Interpret the results of the study seen below ascompletely as you can. If a person had an Openness to Experience Scale score of 6, what would be your bestprediction of that person’s Authoritarianism Scale score? What about an Openness to Experience score of 15? Whatproportion of the variability in Authoritarianism Scale scores is shared with the Openness to Experience Scale? [10pts.]150.885.782.7663.328CountNum. MissingRR SquaredAdjusted R SquaredRMS ResidualRegression SummaryAuthoritarian Scale vs. Openness Scale1 517.722 517.722 46.735 <.000113 144.012 11.07814 661.733DF Sum of Squares Mean Square F-Value P-ValueRegressionResidualTotalANOVA TableAuthoritarian Scale vs. Openness Scale43.402 3.040 43.402 14.277 <.0001-1.759 .257 -.885 -6.836 <.0001Coefficient Std. Error Std. Coeff. t-Value P-ValueInterceptOpenness ScaleRegression CoefficientsAuthoritarian Scale vs. Openness Scale1012.51517.52022.52527.53032.535Authoritarian Scale4 6 8 10 12 14 16 18Openness ScaleY = 43.402 - 1.759 * X; R^2 = .782Regression PlotThere is a significant negative linear relationship between scores on the AuthoritarianScale and the Openness Scale, r = -.885, p < .0001. (Be sure to note how you know that thelinear relationship is significant by pointing to the P-Value and even the F-Value of 46.7.)The two scales share about .78 of their variability, which would be a very large amount forpsychological research (but characteristic of fabricated data such as these).If a person received a score of 6 on the Openness Scale, you would predict a score on theAuthoritarian Scale of:† ˆ y = 43.402 + (-1.759 * 6)ˆ y = 32.8If a person received a score of 15 on the Openness Scale, you would predict a score on theAuthoritarian Scale of:† ˆ y = 43.402 + (-1.759 *15)ˆ y = 17.03. Drs. Frank Lee and Mai Deere were interested in the impact of time on the nature of romantic relationships (i.e.,does familiarity really breed contempt?). To investigate their hypothesis, they recruited 50 people, 10 who had beenin a relationship for 6 months, 10 in a relationship for 12 months, 10 in a relationship for 24 months, 10 in arelationship for 48 months, and 10 in a relationship for 120 months. Each participant was asked to rate the quality ofhis or her relationship on a scale of 1 to 10 (1 = poor and 10 = great). Complete the source table below and interpretthe results of this study as completely as you can. [15 pts]4 83.320 20.830 25.063 <.0001 100.251 1.00045 37.400 .831DF Sum of Squares Mean Square F-Value P-Value Lambda PowerLength of RelResidualANOVA Table for Quality of Rel10 8.900 .994 .31410 9.000 .816 .25810 7.200 .789 .24910 5.600 1.075 .34010 8.500 .850 .269Count Mean Std. Dev. Std. Err.006 mos.012 mos.024 mos.048 mos.120 mos.Means Table for Quality of RelEffect: Length of RelFirst of all, you should note that this study is not a true experiment, in that nothing ismanipulated (or that the people are not assigned to the conditions randomly). As a result,the good doctors would not be justified in making any causal claims.There are significant differences among the ratings at different relationship lengths,F(4,45) = 25.063, p < .0001. In order to determine which specific means differed, you wouldneed to compute a post hoc analysis.† HSD = 4.03.83110= 1.16ComparisonDifferenceH0: m6 = m120.1H0: m6 = m241.7H0: m6 = m483.3H0: m6 = m1200.4H0: m12 = m241.8H0: m12 = m483.4H0: m12 = m1200.5H0: m24 = m481.6H0: m24 = m1201.3H0: m48 = m1202.9Thus, it appears that people in a relationship for 6, 12, or 120 months rated the quality oftheir relationship as significantly higher than people in a relationship for 24 and 48months. People in a relationship for 24 months rated the quality of their relationship assignificantly higher than people in a relationship for 48 months. No other differences weresignificant.4. Drs. Dewey, Screwup, & Howe are industrial/organizational psychologists who were interested in the impact ofnoise levels in the workplace on the productivity of workers. To assess the effect of noise, they went to anautomobile factory, where they could study 10 workers under each of 3 different noise levels (Low, Moderate,High). Their DV was level of productivity (1 = Low to 15 = High). Complete the source table below, then interpretthe results of this study as completely as you can. [15 pts.]9 405.500 45.0562 84.267 42.133 3.747 .0436