Suppose you are assigned the number 1, and the other students in your statistics
ID: 3200336 • Letter: S
Question
Suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. (a) Explain how you could get a random sample of four students from your statistics class. (Select all that apply.) Randomly choose four of the students that are sitting in the back row. Use a computer or random-number table to randomly select four students after numbers are assigned. Randomly choose four of the tallest students in the classroom. Randomly choose four of the last students that walk into the classroom. Randomly choose four of the first students that walk into the classroom. (b) Explain why the first four students walking into the classroom would not necessarily form a random sample. (Select all that apply.) There is nothing wrong with choosing the first four students walking into the classroom. Perhaps they are students with lots of free time and nothing else to do. Perhaps they are students that had a class immediately prior to this one. Perhaps they are excellent students who make a special effort to get to class early. Perhaps they are students that needed less time to get to class. (c) Explain why four students coming in late would not necessarily form a random sample. (Select all that apply.) Perhaps they are students that had a prior class go past scheduled time. Perhaps they are students that need more time to get to class. There is nothing wrong with choosing four students coming in late. Perhaps they are busy students who are never on time to class. Perhaps they are lazy students that don't want to attend class. (d) Explain why four students sitting in the back row would not necessarily form a random sample. (Select all that apply.) Perhaps students in the back row came to class late. Perhaps students in the back row came to class early. Perhaps students in the back row are introverted. Perhaps students in the back row do not pay attention in class. There is nothing wrong with choosing four students sitting in the back row. (e) Explain why the four tallest students would not necessarily form a random sample. (Select all that apply.) Perhaps tall students generally attend more classes. Perhaps tall students generally are athletes. There is nothing wrong with choosing the four tallest students. Perhaps tall students generally are healthier. Perhaps tall students generally sit together.
Explanation / Answer
Solution
Part (a)
i) Randomly choose four of the students that are sitting in the back row.
ii) Use a computer or random-number table to randomly select four students after numbers are assigned.
iii) Randomly choose four of the tallest students in the classroom.
iv) Randomly choose four of the last students that walk into the classroom.
v) Randomly choose four of the first students that walk into the classroom.
Option (ii) is the only correct way of selecting a random sample. In all other cases, the students are of a particular nature which may have direct impact on the objective of the study and hence can be a biased sample.
Part (b)
i) There is nothing wrong with choosing the first four students walking into the classroom.
Ii) Perhaps they are students with lots of free time and nothing else to do.
iii) Perhaps they are students that had a class immediately prior to this one.
iv) Perhaps they are excellent students who make a special effort to get to class early.
v) Perhaps they are students that needed less time to get to class.
Clearly (i) is not acceptable since ‘first four students walking into the classroom’ is a special and specific group and hence the sample would be a biased one.All other options are possible explanations since each forms a special and specific group and hence the sample would be a biased one.
Part (c)
i) Perhaps they are students that had a prior class go past scheduled time.
ii) Perhaps they are students that need more time to get to class.
III) There is nothing wrong with choosing four students coming in late.
iv) Perhaps they are busy students who are never on time to class.
v) Perhaps they are lazy students that don't want to attend class.
Clearly (iii) is not acceptable since ‘four students coming in late’ is a special and specific group and hence the sample would be a biased one. All other options are possible explanations since each forms a special and specific group and hence the sample would be a biased one.
Part (d)
i) Perhaps students in the back row came to class late.
ii) Perhaps students in the back row came to class early.
iii) Perhaps students in the back row are introverted.
iv) Perhaps students in the back row do not pay attention in class.
v) There is nothing wrong with choosing four students sitting in the back row.
Clearly (v) is not acceptable since ‘four students sitting in the back row’ is a special and specific group and hence the sample would be a biased one. All other options are possible explanations since each forms a special and specific group and hence the sample would be a biased one.
Part (e)
i) Perhaps tall students generally attend more classes.
Ii) Perhaps tall students generally are athletes.
iii) There is nothing wrong with choosing the four tallest students.
iv) Perhaps tall students generally are healthier.
v) Perhaps tall students generally sit together.
Clearly (iii) is not acceptable since ‘four tallest students’ is a special and specific group and hence the sample would be a biased one. All other options are possible explanations since each forms a special and specific group and hence the sample would be a biased one.