71 Mean SD Drug 20 3 4 Placebo 16 1 3 H0 Z \"drug \"placeboio' (1 pt) Suppose you have prior evidence that the drug works (the group took the drug should have higher score) then H0 : pdmg uplacebo 0. (1 pt) Which test should you perform (two sample t-test or matched(paired) t-test)? Why? (2 pts) Compute the test statistic. How many df if we want to test conservatively? (3 pts) Find the p-value, and make your conclusion (a = 0.05). (2 pts) Redo part(d) and (e) by R. Please attach your R output. Please use the exact df instead of the conservative one. (5 pts) In fact, based on the prior study we also know that the two groups have the same population standard deviation. Please redo part ((1) and (e). (5 pts) Redo part (g) by R. Please attach your R output. (2 pts) Suppose you made a mistake. When you calculated the pvalue, you used Z table instead of the t table. Would your p-value be bigger or smaller by using the wrong table? Briey state the reason to support your answer. (Hint: you could compare the shape of two distributions, or compare the upper tail probabilities for the same critical value. More specically, t distribution is atter than standard normal and has fatter tail.) (2 pts)