Mike Promesses is going up for reelection. His team of advisers, Peiqi and Wenjie, tell him that, according to a poll conducted two days earlier, the proportion of people who intend to vote for him is given by the confidence interval 53 % i 9.8 % = [43.2%, 62.8%]. Mike Promesses needs 50 % of the votes to be elected and he is now worried. He thinks that in the above condence interval, the 9.8 % margin of error is too large for him to get a clear picture of the situation. Therefore, Mike Promesses asks Peiqi and Wenjie to organise a new survey which would result in a confidence interval with a margin of error of 2.3% = 0.023. Peiqi and Wenjie design a plan: - They want the level of condence for that new condence interval to be 92%. - Also, since the previous poll was only two days earlier, Peiqi and Wenjie expect the proportion of people in the sample who intend to vote for Mike Promesses to be close to 53%. - Based on these pieces of information, they plan to calculate the sample size n needed to ensure that their new condence interval will have a margin of error of 2.3% = 0.023. - Peiqi and Wenjie have noticed that when asked face-to-face, people are more likely to agree to answer the poll then when contacted by phone (some people just hang up). For that reason, they decide that they will go to their local grocery market and poll in, people there. - Finally, they will calculate the new condence interval for the true proportion of the voters who are planning to vote for Mike Promesses. (a) How many people should Peiqi and Wenjie suvey to get a level of confidence of 92%? Sample size : n : [1'] (b) Do you think that about 92% of the condence intervals produced that way will contain the true proportion of voters who are planning to vote for Mike Promesses