Mr. Thomas of Wilmer Amina Carter High School (a large urban high school) wants to know whatproportion 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 AminaCarter 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. Doesthis confidence interval provide convincing evidence that a majority of students favor a ban? Explain.(c) It turns out that the council's simple random sample was originally 165 students, but 13 individuals inthe sample didn't respond because they were on an Environmental Science field trip. Could this changeyour 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 AminaCarter High School who support banning plastic water bottles. Explain what you would expect tohappen to the width of the interval if the sample size was increased to n= 608?

Part 2: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 11. 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