Question 1117421: An administrator at a large university wants to conduct a survey to estimate the proportion of students who are satisfied with the appearance of the university buildings and grounds. The administrator is considering three methods of obtaining a sample of 500 students from the 70,000 students at the university.
a. Because of financial constraints, the first method the administrator is considering consists of taking a convenience sample to keep the expenses low. A very large number of students will attend the first football game of the season, and the first 500 students who enter the football stadium could be used as a sample. Why might such a sampling method be biased in producing an estimate of the proportion of students who are satisfied with the appearance of the buildings and grounds?
b. Because of the large number of students at the university, the second method the administrator is considering consists of using a computer with a random number generator to select a simple random sample of 500 students from a list of 70,000 student names. Describe how to implement such a method.
c. Because stratification can often provide a more precise estimate than a simple random sample, the third method the administrator is considering consists of selecting a stratified random sample of 500 students. The university has two campuses with male and female students at each campus. Under what circumstance(s) would stratification by campus provide a more precise estimate of the proportion of students who are satisfied with the appearance of the university buildings and grounds than stratification by gender?
Answer by solver91311(24713)   (Show Source):
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b. Implementation of selection using random numbers.
Step 1, presuming a campus with 70,000 students would have a system of student numbers: Determine the range of the student numbers, that is, determine the lowest student number of all students currently enrolled and determine the highest student number of all students currently enrolled.
Step 2, create a random number generator that will generate a list of unique numbers in the range determined in step 1.
Step 3, each time a random number is generated, perform two checks: First, check to ensure that the current number has not been used before. Second, check that the number generated corresponds to a student actually enrolled. If either test fails, discard the current number and generate another. If both tests pass, place the student corresponding to that number in the list of students to be surveyed.
Step 4, repeat steps 2 and 3 until the list of students to be surveyed consists of the desired sample size. In the given problem, that would be 500 names.
John
My calculator said it, I believe it, that settles it
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