4.102 Multiple choice: Getting a random sample When we use random numbers to tak

Question

4.102 Multiple choice: Getting a random sample When we use random numbers to take a simple random sample of 50 students from the 20,000 students at a university, a. It is impossible to get the random number 00000 or 99999, since they are not random sequences. b. If we get 20001 for the first random number, for the second random number, that number is less likely to occur than the other possible five-digit random numbers. c. The draw 12345 is no more or less likely than the draw 11111 d. Since the sample is random, it is impossible that it will be nonrepresentative, such as having only females in the sample

Explanation / Answer

To randomise 20,000 students, get a 5 digit number from 00000 to 99999.

as there are 100,000 numbers with that 5 digits, assign 5 numbers each of the 20,000 students.

Hence each first student gets 00000, 00001,00002,00003,00004.

If any of these numbers come from the random numbers table, then it is student 1.

Answer is c)

a) is not the answer as we can get random sequences from 00000 to 99999 using the above method.

b) is not the answer as we can get 20001 again after having drawn that number once.

c) is the answer as 12345 is as likely as 11111 between 00000 and 99999.

d) is not the answer as we can give separate code for females and males with 00000 and 99999. Example any even number can be male and odd number can be female.

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