At a certain university, students who live in the dormitories eat at a common di
ID: 3301124 • Letter: A
Question
At a certain university, students who live in the dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question: Many students believe that the food served in the dining hall needs improvement. Do you think that the quality of food served here needs improvement, even though that would increase the cost of the meal plan? ______ Yes ______ No _______ No opinion a) What is the population of interest? What is the population parameter of interest (that is, what number are you trying to estimate)? b) What sampling plan did the manager use to collect his data? c) In this setting, explain how bias may have been introduced based on the way this sample was selected. That is, explain how those chosen for the sample may be different from those who were not chosen with respect to their answers to the question being asked in the survey. d) How might the sample be selected differently to avoid the bias discussed in part c)? Use one of the methods from the Random Rectangle Activity. e) In this setting, explain how bias may have been introduced based on the way the question was worded. That is, explain how the wording of the question might lead toward a specific answer f) Give an alternative wording to the research question that will avoid the bias discussed in part e)?Explanation / Answer
(a)
The population of interest is the students living in the dormitories. The parameter of interest is the proportion of students who want that quality of food should be improved.
(b)
The sampling plan used here was kind of a stratified sampling, in which he has divided the total number of students into batches of 100.
(c)
This sampling method produces a bias, mainly because of the two reasons.
Firstly, because the first 100 students were surveyed, there is a possibility that they like the food, since they were on time as compared to those who came later after them.
Secondly, those who come first will eventually get a slightly better food quality with the food being served hot and fresh to them.
(d)
A better sampling technique would be to ask some students randomly in the mess every hour. If the lunch time duration is 3 hours, then you can ask 33 students randomly selected every hour in the mess.
Hope this helps !
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