com/at/servlet/quiz?quiz_action=takeQuiz&quiz_probGuid=QNAPCOA801010009003138fe80 0606 DO&Ctx=Cynthia.maier-0016&c Assume that roommate B's probability assignments are correct. Roommate B would like to use the hand signal with the highest probability of winning the game. What would you advise roommate B to use? You can simulate a play of the game by basing the game's result on roommate B's probability assignments. That is, the chance that roommate A chooses rock is P(RA), the chance that he chooses paper is P(PA), and the chance that he chooses scissors is P(SA), where P[RA), P(PA), and P(SA) have been previously determined. Okay, play it now! (Click the red PLAY! icon to reveal roommate A's choice.) PLAYI If roommate B took the advice to choose the highest probability of winning, then roommate B 9 20 F3 E # % A &4 assigning probability to events - Rock-paper scissors A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each person Scissors simultaneously displays a hand signal to Indicate a rock, a piece bamis pope of paper, or a pair of scissors. Rock beats scissors, scissors beats paper, and paper beats rock. If both players select the same hand signal, the game results In a tie. Paper beats mori Two roommates, roommate A and roommate B, are about to go cruising with a mutual friend and are arguing over who gets to sit in the front seat. Roommate A suggests a game of rock-paper-scissors to settle the dispute. Rock beats scissors Consider the game of rock-paper-scissors to be a random experiment. How many outcomes are in the sample space of this random experiment? 0 9 0 12 0 2 0 5 Assume that both roommates' choices of rock, paper, or scissors are random, independent, and equally likely. Let RA, Ra, Pa. Pp. SA, and So denote roommate A choosing rock, roommate B choosing rock, roommate A choosing paper, roommate B choosing paper, roommate A choosing scissors, and roommate B choosing scissors, respectively. Additionally, let the simple event consisting of roommates A and B both selecting rock be denoted parenthetically as (RA Ra), and so on for the other possibilities. Define event B as the event that roommate B wins the game and gets to sit in the front seat. Event B is composed of the following simple events: O B - ((Ra, Ral. (RA Po), (PA. 58). (54, Ral) O B - {(BA Sak, (PA. Re), (54, Pal) O B = (RA Pal, (PA. SE)) FULTOOGOWR W 9 20 44 DII FT F9 E # % & 63The term verbally referred to as "y hat" in a regression denotes: 1. y values of hypothetical points located on the regression line 1. the intercept 1. variance not explained by the regression model O 1. residualsA general social survey questioned people on their happiness and familyr income. The data are shown in Table 1. Table 1: Frequencies in happiness and income categories Income Not too happy Pretty happy Very happy Total Above average H 159' 1111] 290 Average 53 3?? 2.11 E46 Below average 94 249 83 426 TUI'AL 1&8 F30 414 1362 {a} Is this an example of a randomised experiment or an observaijonal study? Explain your answer. [bi 1liilhat proportion of people with Above average income are 1very happy? [c] What proportion of people who are Not too happy have Below average income? {d} 1Ilv'hat proportion of people have Average income and are Not too happy? Thank you Programming with R ( in R studio ), PLEASE ANSWER THE QUESTION WITH COMMENT and DETAIL explanation using R programming PLEASE UPLOAD R programming CODE 1. A product development engineer is interested in determining if the cotton weight in synthetic fiber affects the tensile strength, and he has run a completely randomised experiment with five levels of cotton weight percentage and five replicates. Test the hypothesis that cotton weight percentage in the fiber significantly affects the mean tensile strength or not at 5% and 1% level of significance. Weight Observed Tensile Strength (Ib/in?) Percentage N 3 5 of Cotton 15 7 7 15 11 9 20 12 17 12 18 18 25 14 18 18 19 19 30 19 25 22 19 23 35 7 10 11 15 11