Answer this question in R. Show as much of your work as possible. For some reason, you've decided to play a game of Monopoly with your friends.After what seems like one too many “lucky" rolls in a row, you start to think thatone of your friends is cheating. After nearly 10 hours of playing, each of your friendsfall asleep. You decide to take advantage of the situation and test the hypothesisthat the two, six-sider dice are fair. You roll the two dice 1000 times, noting thesum of the two dice each time. The table below shows the results of your 1000rolls. Is there any evidence that these dice are unfair?Sum 2 3 4Count 40 58 8851096 78 9 10 11 12164 135 95 80 63 20148

The observed frequencies for the sum of two dice are given as follows:Sum23456789101112Count40588810914816413595806320In order to validate if the two dice are fair, the deviation between the theoretical frequencies and the experimental frequencies of the sum of the faces of the two dice are to be considered. For this, the Chi-square goodness of fit is to be formulated.It is hypothesized as follows:H0: The two dice are hypothesized to be not unfair.H1: The two dice are hypothesized to be unfair.This is to be noted that, as under the H0, the dice are hypothesized to be fair in nature, the probability of having each of the sum remains the same, i.e., P(2)=P(3)=P(4)=P(5)=P(6)=P(7)=P(8)=P(9)=P(10)=P(11)=P(12)=111.The Chi-square test is carried out using R as follows:1 2### Observed number of counts #### 3obs<- c(40,58,88,109,148,164,135,95,80,63,20) 4 5#### Expected number of counts; in terms of probability #### 6e_prop<- c(1/11,1/11, 1/11, 1/11, 1/11, 1/11, 1/11, 1/11, 1/11, 1/11, 1/11 ) 7## each sum has probability of 1/11 of landing ### 8 9 10### Chi-square test ### 11chisq.test(obs, p=e_prop)The result is obtained as follows:1 Chi-squared test for given probabilities 2 3data: obs 4X-squared = 225.49, df = 10, p-value < 2.2e-16 5The p-value is 0.0000 approximately. The decision rule is: "Reject H0, if p-value≤α".For any significance level of α=0.01, 0.05, or 0.10, p-value (=0.0000)<α. Thus H0 is rejected.The two dice are concluded to be unfair.The sample provides sufficient reason to believe that the dice are unfair.