Question ] To settle a debate over whether Coca Cola or Pepsi Cola is more popular, a random sample of 79 participants was selected and asked to state their preference for one of the drinks. 43 of them preferred Coca Cola. Let p denote the proportion of the population who prefer Coca Cola. (a) Compute the probability that a participant selected at random from the sample will prefer Coca Cola. (1 mark) (b) What is the probability that two participants selected (without replacement) at random from the sample will both prefer Coca Cola? (3 marks) (c) Construct a 95% condence interval for p. (4 marks) (d) Construct a one-sided 95% condence interval for p of the form (r, 1). (3 marks) (e) What conclusion about p can be drawn from these confidence intervals? In particular, can we claim that Coca Cola is the more popular drink? That is, is p > 0.50? (3 marks) Suppose the sample size is increased to 7,900 participants (100 timeS), and the sample proportion stays the same at 13 = :23; (f) What impact does the bigger sample have, if any, on the standard deviation of p"? (3 marks) (g) Will the enlarged sample size affect your answer in Question 1(e)? If so, in what manner