12. Mr. Thomas of Wilmer Amina Carter High School (a large urban high school) wants to know what proportion of the student body favors banning plastic water bottles from the school buildings and grounds. A simple random sample of 152 students finds that 85 support banning plastic bottles. (a) Construct and interpret a 95% confidence interval for the proportion of all students at Wilmer Amina Carter High School who support banning plastic water bottles. (b) The student council will ban the bottles if they are convinced that the majority of students favor it. Does this confidence interval provide evidence for a ban? Explain. (c) It turns out that the council’s simple random sample was originally 165 students, but 13 individuals in the sample didn’t respond because they were on an Environmental Science field trip. Could this change your answer to part (b)? Explain your reasoning with a calculation. (d) In part (a) you constructed a 95% confidence interval for the proportion of students at Wilmer Amina Carter High School who support banning plastic water bottles. Explain what you would expect to happen to the length of the interval if the sample size was doubled.

Mobon oil company owns a lease that entitles it to explore for oil on a parcel of offshore land in california. since the lease is about to expire mobon must now decide whether to drill for oil at the site or to sell the lease to excel oil company, which has just offered mobon $50,000. mobon estimates it would cost $100,000 to drill at the site. if the well were dry, all this cost would be lost. if the well were successful, its value to mobon would depend on the extent of the oil discovered. for simplicity, mobon assumes there are only two types of successful wells: minor and major success. mobon estimates that a minor success would result in revenues of $200,000 in excess of the drilling cost, whereas a major success would result in revenue of $500,000 in excess of the drilling cost. mobon has assessed the following probabilities: if the well is dry then the probability is 0.7, if it is a minor success the probability is 0.2, and if it is a major success the probability is 0.1. a) construct an appropriate payoff matrix, b) using the maximax criterion, identify the optimal decision c) using the maximin criterion, identify the optimal decision d) using the minimax criterion, identify the optimal decision e) using the emv criterion, identify the optimal decision