To gather information about the validity of a new...

To gather information about the validity of a new standardized test for tenth-grade students in a particular state, a random sample of 15 high schools was selected from the state. The new test was administered to every 10 th-grade student in the selected high schools. What kind of sample is this? (a) A simple random sample (b) $A$ stratified random sample (c) A cluster sanple (d) $A$ systematic random sample (e) A voluntary response sample

To gather information about the validity of a new standardized test for tenth-grade students in a particular state, a random sample of 15 high schools was selected from the state. The new test was administered to every 10 th-grade student in the selected high schools. What kind of sample is this?
(a) A simple random sample
(b) $A$ stratified random sample
(c) A cluster sanple
(d) $A$ systematic random sample
(e) A voluntary response sample

Key Concepts

Cluster Sampling

Cluster sampling is a method where the population is divided into naturally occurring groups, or clusters, such as schools, neighborhoods, or geographic areas, and a random selection of these clusters is chosen. All individuals within the selected clusters are then surveyed. This approach is often used when it is logistically or economically impractical to compile a complete list of the entire population and when clusters represent natural groupings of the population.

Simple Random Sampling

Simple random sampling is a technique in which every member of the population has an equal chance of being selected, typically requiring a comprehensive list of the entire population. It ensures that each possible sample is equally likely, making it one of the most straightforward methods for obtaining a representative sample in theory, though it can be challenging to execute with large or dispersed populations.

Stratified Sampling

Stratified sampling involves dividing the population into distinct subgroups or strata based on a specific characteristic and then drawing a random sample from each stratum. This method ensures that each subgroup is adequately represented in the final sample, which is particularly useful when researchers want to examine differences among subgroups within the population.

Systematic Sampling

Systematic sampling is a method where a random starting point is chosen and subsequent elements are selected using a fixed interval, such as every kth individual from a list. This method is simpler to perform than simple random sampling, but care must be taken to ensure that the list does not have an underlying pattern that could bias the sample.

Voluntary Response Sampling

Voluntary response sampling is a sampling technique where individuals self-select to participate in a survey or study, such as by responding to an advertisement or invitation. While this method is easy to implement, it often leads to biased results because it tends to attract participants who have strong opinions or are particularly motivated to respond, which may not represent the views of the entire population.

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