Question 1 :Let X1, . . . , Xn be be i.i.d. with Bernoulli(p). Derive a left-hand-sided confidence interval for p. Use a pivot quantity that follows Normal distribution. An

approximation or central limit theorem can be applied to get the pivot quantity.

Question 2

When flipping a penny or spinning a penny, is the probability of getting heads the same? Use the data from the following table. Heads Tails Flipping 2048 1992 Spinning 953 1047 (a) Use a 0.05 significance level to test the claim that the proportion of heads is the same with flipping as with spinning. (b) Which method is used above and why. Is there any other method that could have also been used if yes, why. If not, why not. (c) In general, how do you find a rejection region in such tests. Explain