Which sampling method was used in each of the following settings, in order from I to IV?

I. A student chooses for a survey the first $20$students to arrive at school.

II. The name of each student in a school is written on a card, the cards are well mixed, and $10$names are drawn.

III. A state agency randomly selects $50$people from each of the state’s senatorial districts.

IV. A city council randomly selects eight city blocks and then surveys all the voting-age residents of those blocks.

(a) Voluntary response, SRS, cluster, stratified

(b) Voluntary response, SRS, stratified, cluster

(c) Convenience, cluster, SRS, stratified

(d) Convenience, SRS, cluster, stratified

(e) Cluster, SRS, stratified, convenience

We need to find out that, which sampling method is used in each of the settings in order from I to IV

We know that,

Convenience sampling uses for example voluntary response or a subgroup from the population i.e. without any biasness

Simple random sampling(SRS) uses a sample in which every individual is given equal chance for being chosen

Stratified randomized sampling draws simple random samples into small independent groups

Cluster sampling divides the population into smaller non-overlapping groups and some of these subgroups into samples

Therefore we note that sampling methods used are as below,

I. A simple sample or sample of voluntary response, because the first 20 students are easily selected.

II. Simple random samples, because every individual is given equal chance.

III. Stratified random sampling, because the independent subgroups are states.

IV. Cluster sampling, because the subgroups are the city blocks.

Hence, the correct option is (b).