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.