Here we are going to test a couple of hypotheses about the Old Faithful data in R. Remember, this is the faithful data frame that is built in to R. You can use data (faithful) to load data set. First split faithful into two separate data frames: (1) those entries with eruption times less than 3 minutes (eruptions < 3) and (2) those entries with eruption times greater than or equal to 3 minutes (eruptions >= 3). Answer the following about the entry wait time (waiting): (a) For the entries with short eruption times, you want to test the hypothesis that the associated waiting last on average less than 60 minutes. What is the null hypothesis? What is the alternative hypothesis? (Write your own code) (10 pt) (b) Give R commands to compute the statistic that you used in (a) and the resulting p-value. What values did you get? Would you reject the null hypothesis at the a = 0.05 level? (15 pt) (c) For the entries with long eruption times, you want to test the hypothesis that the associated waiting time last on average shorter than 80 minutes. What is the null hypothesis? What is the alternative hypothesis? (Write your own code) (10 pt) (d) Give R commands to compute the statistic you used in (c) and the resulting p-value to test the hypothesis you came up with in part (c). What values did you get? Would you reject the null hypothesis at the a= 0.05 level? (15 pt)