1. A small undergraduate college has 1,000 students, evenly distributed among the four classes:freshman, sophomore, junior and senior.A study is being designed to estimate the percentageof students in the college who own a cellular phone.It is decided to interview a sample of 100students.One student proposes the following method for selecting the sample: Write the nameof each student on a ticket, put the 1,000 tickets in a box, stir them up so they are thoroughlymixed, and then take 100 tickets at random from the box.Another student objects on thegrounds that this sample is unlikely to have exactly 25 students in each of the four classes.So,a second design is proposed: Hire a team of four interviewers, one from each class, and askeach interviewer to select 25 representative students from their class.(a) Which method of sampling is preferred in this situation?Why?(b) Can you suggest a better method of sampling in order to ensure that exactly 25 studentsfrom each class are contained in the sample?2. A forester wanted to survey spruce trees on one face of a mountain in order to determine thepercentage of spruce trees that were infested or were attacked by a very destructive insectknown as the tomentosus.The forester obtained a map of the mountain and then subdividedthe area of interest into 400 square grids with each square covering an area of 100 squaremetres.A simple random sample of 50 squares was selected, and for each selected square,the survey team determined the total number of spruce trees and the number of such trees thatwere infested or had been attacked by the tomentosus.(a) Identify the parameter that the forester was interested in.(b) What sampling design was used for this survey?(c) If the tomentosus is believed to be evenly distributed throughout the face of this mountain,would you recommend this sampling design?Why or why not?(d) If the tomentosus prefers to reside in regions of the mountain face with higher temperaturesand hence lower elevations, would you recommend using a different sampling design?Explain your answer briefly.