[3] [4] 7. In a previous example we examined the relationship between presence of a specic gene allele and cilantro preference. We were able to come up with an argument suggesting the two factors were related, but we didn't yet have the tools to conduct a formal hypothesis test. Now we can approach this problem with more rigor. Here is the table of data from this experiment: Has Allele Does Not Have Allele Likes Cilantro 18 50 Dislikes Cilantro 31 20 Table Q7: Contingency Table for the Cilantro Study. A participant in the study is selected at random. Consider the following events: A : The participant likes cilantro. B : The participant has the allele. (a) 'Nhat is the probability that a randomly selected participant likes Cilantro, P(A)? (b) What is the probability that a randomly selected participant has the allele, P(B)? [0) Recall that if events A and B are independent, then the probability of A AND B , P(A AND B) is given by P(A)P(B). Also recall that A' represents the probability that event A does not happen. Using the probabilities from parts a) and b), deter mine the following probabilities assuming A and B are independent: P(A AND B), P(A AND 3'), P(A' AND B), P(A' AND B') (d) Conduct a Test of Independence to determine whether the factors L'Likes Cilantro\" and L'Has the Allele\" are independent. Use a signicance threshold of o: = 0.05. State all relevant hypotheses and test statistics/ distributions, as well as the p-value and appropriate conclusion of the test. You may use geogebra to help out with computations for this problem. Please also show how to calculate the x2 statistic using the data from Table Q7 and your calculations from part c). Hint: You might nd it useful to check the boxes beside \"Expected Count\"1 and \"x2 contribution\