Question

37. Simple Random Sample vs. Random Sample Refer to the definition of simple random sample on page 27 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 shuµed and six names are drawn from the top.

C. For the same class described in part (a), the six youngest students are selected.

Can someone explain does die play a part in part a if it is Random sample or A simple random sample or not?

Thank you

Answer 1

a) This is the case of stratified random sampling which is a type of random sampling. Here the die is not playing any part as the sampling method is already determined and due is just making the simple random sampling of these strata. Also remember here all the samples have not a equal probability.

b) Here all the random samples have equal probability i.e. 1/6. Hence this is the case simple random sampling.

c) This is neither a simple random sampling nor a random sampling as here we're choosing selected members from the sample.