Consider the students in your statistics class as the population and suppose the
ID: 3271965 • Letter: C
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 two rows as your sample. If it comes up tails, you use the 20 students sitting in the last two rows as your sample. (a) Does every student have an equal chance of being selected for the sample? Explain. No, the coin flip does not ensure an equal chance of being selected. No, your seating location does not ensure an equal chance of being selected. Yes, your seating location and the randomized coin flip ensure equal chances of being selected. Yes, your seating location ensures an equal chance of being selected. (b) Is it possible to include students sitting in row 3 with students sitting in row 2 in your sample? No, it is not possible with this described method of selection. Sometimes it is possible with this described method of selections. Yes, it is possible with this described method of selection. Is your sample a sample random sample? Explain. No, this is not a simple random sample. It is a cluster sample. No, this is not a sample random sample. It is a systematic sample. Yes, this is a sample random sample. No, this is not a sample random sample. It is a stratified sample. (c) Describe a process you could use to get a sample random sample of size 20 from a class of size 40. Assign each student a number 1, 2, ... , 20 and use a computer of a random-number table to select 10 students. Assign each student to a pair 1, 2, ... , 20 and use a computer a random-number table to select 10 pairs. Assign each student a group 1, 2, 3, 4 and use a computer or a random-number table to select 2 groups. Assign each student a number 1, 2, ... , 40 and use a computer or a random-number table to select 20 students.Explanation / Answer
Solution:
a) Yes, your seating location and the randomized coin flip ensure equal chances of being selected.
The chance for a student to be selected for the sample = 1/2 *1/20 = 1/40
Hence, we can say that every student has an equal chance of being selected for the sample.
b) No, when a coin is tossed, if head comes up, first two rows will be included and when tail comes uo last two rows (3rd and 4th rows) will be included into the sample.
There is no possibility of including 2nd rwo and 3rd row with the given coin experiment.
Hence, we cannot include students sitting in row 3 with students sitting in row 2 in our sample.
When a coin is tossed two different set of rows are selected randomly but the students in the rows are taken directly. A sequence of students will be there in the sample.
Here randomized rows are selected but students are not selected randomly. Hence, it is not a simple random sample.
c) We assign each student a different number between 1 and 40, inclusive. Then use random number table to choose the sample.
We randomly start at one point and select numbers from the table. Since the highest number is 40, we skip the numbers that are greater than 40.
In this example, from table 1, starting at line 16, our chosen 20 two-digit random numbers are
29 31 32 13 02 18 10 17 20 23 12 26 08 10 06 07 22 35 11 40 15
Students bearing the above numbers are included into the sample.
This constructs the simple random sample of size 20.