Please find the question attached in two following screen shots:

Problem 3 (20 points). Are gender and grade associated? To answer this question, a statistics instructor summarizes the grades in one of his small classes as follows: Gender female male Grade pass 18 16 fail 2 4 For the following questions, please show the key steps of your solutions but keep your answers concise. (a) (14 points) (1) Write down the null and alternative hypotheses in words. Use the Fisher's exact test and the X2 test to test the independence between gender and grade respectively. For each method, rst do the calculations by hand (with a calculator), and then conrm your results by using R functions. Use a signicant level 0.05. You may use a one-sided test if necessary. (b) (6 points) (i) Which method in (a) may give more reliable conclusions for this dataset? Briey state your reason in one or two sentences. (ii) In (a), how to draw a conclusion if the two methods give very different results? What does it imply when the two methods give similar results? Limit your answer to each question in one or two sentences. (iii) Why are you asked to do the calculations by hand when software is available and easy to use? Limit your answers in one or two sentences