question

Explain the difference between a stratified sample and a cluster sample

answer

In a stratified sample, random samples from each strata are included.
In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.

question

Explain the difference between a simple random sample and a systematic sample.

answer

In a simple random sample, every sample of size n has an equal chance of being included.
In a systematic sample, the only samples possible are those including every kth item from the random starting position

question

Consider the students in your statistics class as the population and suppose they are seated in four rows of 10 students each. To select a sample, toss a coin. If it comes up heads, you use the 20 students sitting in the first two rows as your sample. If it comes up tails, you use the 20 students sitting in the last two rows as your sample.
1)Does every student have an equal chance of being selected for the sample? Explain.
A)Yes, your seating location ensures an equal chance of being selected.
B)Yes, your seating location and the randomized coin flip ensure equal chances of being selected.
C)No, the coin flip does not ensure an equal chance of being selected.
D)No, your seating location does not ensure an equal chance of being selected.
2)Is it possible to include students sitting in row 3 with students sitting in row 2 in your sample?
A)Sometimes it is possible with this described method of selections.
B)Yes, it is possible with this described method of selection.
C)No, it is not possible with this described method of selection.
3)Is your sample a simple random sample? Explain.
A)No, this is not a simple random sample. It is a cluster sample.
B)No, this is not a simple random sample. It is a stratified sample.
C)Yes, this is a simple random sample.
D)No, this is not a simple random sample. It is a systematic sample.
4)Describe a process you could use to get a simple random sample of size 20 from a class of size 40.
A)Assign each student to a pair 1, 2, . . . , 20 and use a computer or a random-number table to select 10 pairs.
B)Assign each student a number 1, 2, . . . , 40 and use a computer or a random-number table to select 20 students.
C)Assign each student a group 1, 2, 3, 4 and use a computer or a random-number table to select 2 groups.
D)Assign each student a number 1, 2, . . . , 20 and use a computer or a random-number table to select 10 students.

answer

1)B
2)C
3)A
4)B

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.
1)Explain how you could get a random sample of four students from your statistics class. (Select all that apply.)
A)Use a computer or random-number table to randomly select four students after numbers are assigned.
B)Randomly choose four of the last students that walk into the classroom.
C)Randomly choose four of the students that are sitting in the back row.
D)Randomly choose four of the tallest students in the classroom.
E)Randomly choose four of the first students that walk into the classroom.
2)Explain why the first four students walking into the classroom would not necessarily form a random sample. (Select all that apply.)
A)Perhaps they are excellent students who make a special effort to get to class early.
B)Perhaps they are students that needed less time to get to class.
C)There is nothing wrong with choosing the first four students walking into the classroom.
D)Perhaps they are students that had a class immediately prior to this one.
E)Perhaps they are students with lots of free time and nothing else to do.
3)Explain why four students coming in late would not necessarily form a random sample. (Select all that apply.)
A)Perhaps they are students that had a prior class go past scheduled time.
B)Perhaps they are lazy students that don't want to attend class.
C)Perhaps they are busy students who are never on time to class.
D)There is nothing wrong with choosing four students coming in late.
E)Perhaps they are students that need more time to get to class.
4)Explain why four students sitting in the back row would not necessarily form a random sample. (Select all that apply.)
A)Perhaps students in the back row came to class late.
B)There is nothing wrong with choosing four students sitting in the back row.
C)Perhaps students in the back row came to class early.
D)Perhaps students in the back row are introverted.
E)Perhaps students in the back row do not pay attention in class.
5)Explain why the four tallest students would not necessarily form a random sample. (Select all that apply.)
A)Perhaps tall students generally sit together.
B)Perhaps tall students generally are athletes.
CPerhaps tall students generally attend more classes.
D)Perhaps tall students generally are healthier.
E)There is nothing wrong with choosing the four tallest students.

answer

1)A
2)A,B,D,E
3)A,B,C,E
4)A,C,D,E
5)A,B,C,D

question

In the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted.
The population consists of all 250 students in your large statistics class. You plan to obtain a simple random sample of 30 students by using the sampling frame of students present next Monday. (Select all that apply.)
A)Students who are skipping class cannot be sampled.
B)Home-schooled students cannot be sampled.
C)Students who are not taking statistics cannot be sampled.
D)Dropouts cannot be sampled.
E)Students who are on a school trip cannot be sampled.
F)Students who are out sick cannot be sampled.

answer

A,E,F

question

In the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted.
The population consists of all 15-year-olds living in the attendance district of a local high school. You plan to obtain a simple random sample of 200 such residents by using the student roster of the high school as the sampling frame. (Select all that apply.)
A)Dropouts cannot be sampled.
B)Students who are out sick cannot be sampled.
C)Students who are skipping class cannot be sampled.
D)Home-schooled students cannot be sampled.
E)16-year-olds cannot be sampled.
F)Students who are on a school trip cannot be sampled.

answer

A,D