Question

A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows:

a. Simple Random Sampling
b. Systematic Sampling
c. Stratified Sampling
d. Cluster Sampling

Answer 1

Random sampling methods are various ways to select representative samples from a population, including simple random, stratified, systematic, and cluster sampling. Each method is used to accurately estimate population characteristics, with examples provided to illustrate the use of each method.

Step-by-step explanation:

The subject matter discussed here pertains to different methods of random sampling used to estimate population parameters using a sample. Random sampling methods mentioned include simple random sampling, systematic sampling, stratified sampling, and cluster sampling. These methods are designed to obtain a representative sample from a larger population to ensure that the sample contributes to a more accurate estimation of the population characteristics.

• Simple random sampling is when every member of the population has an equal chance of being included in the sample, similar to drawing names from a hat.
• Stratified sampling involves dividing the population into strata or groups and then taking a sample from each stratum.
• Systematic sampling requires selecting a sample from the population at regular intervals, like every tenth customer.
• Cluster sampling involves selecting entire groups or clusters randomly, then examining each member within these clusters.

For example, if a manager selects four departments at random and interviews all employees in those departments, the type of sampling used is cluster sampling. Similarly, when a soccer coach picks players from different age groups to form a team, it is a case of stratified sampling. Choosing a sample by selecting a set number of individuals from each class, as in the case with Lake Tahoe Community College math classes, is also an example of stratified sampling.

Answer 2

The question pertains to different random sampling methods, which include simple random sampling, stratified sampling, cluster sampling, and systematic sampling, each with unique processes and use cases in statistics.

Step-by-step explanation:

The question being asked is about different methods of sampling used in statistics to represent a population. There are four main types of random sampling methods that can be used. A simple random sample gives each member of the population an equal chance of being selected. In stratified sampling, the population is divided into groups known as strata and a random sample is taken from each stratum. Cluster sampling involves dividing the population into clusters, and then randomly selecting whole clusters and using all individuals within those clusters for the sample. Lastly, systematic sampling is a method where you select every 'k-th' member from a list or sequence to be included in the sample.

For example, in the exercise involving the department store manager measuring employee satisfaction by conducting interviews with all employees in four randomly selected departments, this is an example of cluster sampling. Similarly, when an instructor takes a sample by gathering data on five randomly selected students from each math class, this is an example of stratified sampling.