Please solve

5. In a summer tea-part in Cambridge, England, a lady claimed to be able to discern, by taste alone, whether a cup of tea with milk had the tea poured rst or the milk poured rst. An experiment was performed by Sir R. A. Fisher, then and there, to see if her claim is valid. Eight cups of tea are prepared and presented to her in random order. Both Sir R. A. Fisher and the lady know that four had the milk poured rst, and four had the tea poured rst. The lady tasted each one and rendered her opinion. The results are summarized in a 2x2 table: Poured rst \"1- --n (a) {2 pts) Is the sampling in this study full Mnltinolnial sampling, product Multinomial sam- pling, or Hypergeometric sampling? [b] (3 pts) What is the probability of observing these counts (the data)? (c) (2 pts) We want to conduct a test on the following hypotheses: Hg : The lady has no discerning ability vs H1 : Otherwise Find the four expected counts (or their estimates) under the Ho. You do not need to derive these from scratch, if your intuition 3' reasoning makes sense. [d] {2 pts) Conduct the test by computing appropriate test statistic and critical value at the or = 0.05 level. [e] (2 ptsl Conduct the same hypothesis test by computing the pvalue. (f) (3 pts) If we assume that the lady actually has the discerning ability (i.e., in the direction of H1], which values of the counts {$u,.1712,$21,$22) do you anticipate to see in the table above? What is the probability of observing these counts