b] (4 points) You are interested in testing whether a population central value of your distribution is greater than 19.6 minutes. Please write down which population central value that we discussed in class is most appropriate in this context and also write down the corresponding null and alternative hypotheses for the hypothesis test you will proceed with. c] (3 points] Consider the scenario in part b], and assume that the value of the test statistic you obtained was 15. Find the appropriate critical value for this test, make a decision, and be sure to write out a full conclusion. Please assume that a = 0.05. 5) (10 points] As an overconfident chess player, you record the amount of time [minutes] it took you to beat your opponent. After tallying n = 20 wins over the previous year, you visualize your data using the following histogram: Time to Victory . 19.2 19.4 19.6 19.3 20.0 Time Y = 19.76 minutes 3 = 0.235 Shapiro Wilk Test P value = 0.0019 a) (3 points) Is it appropriate to conclude that your data follow a normal distribution? Please be sure to explain all the appropriate statistics or plots that were used to arrive at your conclusion. Assume a = 0.05