Question

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.

1. 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.

Short answer

a. The sample of students arranged according to the numbered rows and the outcome of the die is a random sample only.

b. The sample of students selected according to the name on the shuffled card is both a random sample and a simple random sample.

c. The sample of the six youngest students is neither a simple random sample nor a random sample.

Step-by-step solution

Given information

Three different samples are provided, and they are to be categorized as simple random samples or random samples.

Simple random sample and random sample

Arandom sample is considered as a sample where the observations/units of the sample are randomly chosen and not as per the biased and selective choice of the experimenter. For example, 100 hats are chosen at random.

A simple random sample is one where all the subjects/observations of the sample have an equal chance of selection and allocation to any of the available units. For example, out of the 100 hats, each hat has a number printed on it starting from 1 to 100. There is an equal chance of selecting a hat numbered 1 to 100.

Identify the type of sample used in the different cases

The students are selected randomly, but they do not have an equal chance to sit in any of the numbered rows. This is because the number of the row is decided by the number on the die. Thus, this sample is random.

b.

The students are selected randomly, and there is an equal chance for each of the 36 students to be selected out of the six shuffled cards drawn. Thus, this sample is botha random sample and a simple random sample.

c.

The students are selected according to their age. Older students have no chance of getting selected. Thus, this sample isneither a random sample nor a simple random sample.