(3) A student claims to be able to distinguish the taste of Alpha coffee from Beta coffee, even though his friends say the two coffees are the same in appearance, aroma, and taste. The student agrees to take a blind taste test consisting of 100 trials as follows. On each trial, the student is given two identical unmarked cups (small ones!), one con taining Alpha coffee and the other containing Beta coffee. He is not told which is which. He has to drink the contents and say which one is Alpha. The student picks correctly on 60 out of the 100 trials. He says that his friends now have to accept his claim. His friends say they will do no such thing because he could just have been guessing at random. Decide which position is better supported by the data, in the following steps. (a) [lpt] State an appropriate null hypothesis in nontechnical terms and also as a set of assumptions about random variables. (b) [1pt] State an appropriate alternative hypothesis. (c) [1pt] What test statistic are you going to use? Justify your choice. (d) [1pt] Using CLT, find an approximated p-value. (You may use Python with 'stats.norm.cdf' function in 'SciPy' package. ) (e) [1pt] At the 5% level, what is the conclusion of the test? Why? Use the p-value in (d)