Refer to the definition of simple random sample available below and its accompanying definition of random sample enclosed within
parentheses. Determine whether each of the following is a simple random sample and a random sample. a. A statistics class with 36 students is arranged so that there are 6 rows with 6 students in each row, and the rows are numbered from 1 through 6. A die is rolled and a sample consists of all students in the row corresponding to the outcome of the die. b. For the same class described in part (a), the 36 student names are written on 36 individual index cards. The cards are shuffled and six names are drawn from the top. c. For the same class described in part (a), the six youngest students are selected.
a) This would be a simple random sample given that the dice roll is a random method to select the students and the probability of each outcome of the dice is 1/6.
b) This would be a random sample, given that the cards are shuffled, this is a random event. However, there's a condition on how to select the cards (The top ones are chosen) and therefore this can not be a simple random sample since not all cards have the same probability of being selected.
c) This is not a random sample since there is an specific condition on how to choose the students (by their age)
