how can i solve this q , as can as possible

Two statisticians, Ramon and Fernando, share salsa dancing as another common interest. Ramon claims that it is well known in the dancing community that he is a better dancer than Fernando. To test this hypothesis, they first agree that the best dancer is he who gets the smallest proportion of rejections (a lady can either accept or reject a dance invitation) over the course of one month. After one month, Ramon reports that out of 58 dance invites, he got 51 accepted. Fernando reports that out of 53 dances, he got 44 accepted. (a.) (1 mark) Carefully state the models, including the assumptions, that you would use to carry out a statistical analysis of the situation described above.(b.) (2 marks) Write down the null and alternative hypotheses to test Ramon's claim. (c.) (3 marks) Given your hypothesis in (b.), explain in words the two different errors that may result from this analysis? From Ramon's ego's point of view, which of these errors do you think is worse to commit? (d.) (3 marks) Provide a 95% confidence interval for the proportion in the dance community that would reject a dance from Fernando. Interpret the interval. (e.) (4 marks) Test your hypothesis in (b.) using the significance level a = 0.05. What is your conclusion regarding who is the better dancer? (f.) (2 marks) Suppose that the power of the test is 0.78 if the true population proportion that rejects a dance from Fernando is 0.14, and the corresponding population proportion for Ramon is 0.10. What is the probability of Type II error in this case