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Professors A college administrator wants to determine whether the professors at the college are doing a good job. Each professor teaches multiple classes, and so for each professor, one of his or her classes is randomly chosen, and all the students are surveyed to find out their opinion of the teacher. What kind of sampling is this?

Short Answer

Expert verified
The described sampling method is 'Cluster Sampling'

Step by step solution

01

Identify the sampling process

Firstly, it is important to understand the sampling process described in the question. The college administrator is choosing professors and then for each chosen professor, one class is randomly picked. Then, every student in that class is surveyed.
02

Compare sampling process with known sampling methods

Now compare this process with known sampling methods. There are several types of sampling methods including simple random sampling, systematic sampling, stratified sampling and cluster sampling. In this case, a group (a professor's class) is randomly chosen and every member (student) of this chosen group is surveyed. This process corresponds to 'cluster sampling'.
03

Confirm the type of sampling

In cluster sampling, the total population is divided into these groups (or clusters) and a simple random sample of the groups is selected. If a sampling unit is a group of similar elements or units, the sampling technique is called cluster sampling. So this process can be confirmed as cluster sampling.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sampling Methods
Sampling methods are techniques used to select a representative subset of a larger population, which is necessary for conducting studies without the need for a full census. Different methods suit different types of research objectives and constraints such as time, budget, and the nature of the population. Some common sampling methods include simple random sampling, stratified sampling, and cluster sampling.

While simple random sampling provides each member of the population an equal chance of being selected, stratified sampling involves dividing the population into subgroups and selecting samples from each stratum. Cluster sampling, on the other hand, selects intact units, or clusters, at random, then examines all individuals within the selected clusters. Systematic sampling, another method, involves choosing subjects at regular intervals from an ordered population. The choice of sampling technique impacts the accuracy, bias, and generalizability of the study's findings.
Simple Random Sampling
Simple random sampling (SRS) is a fundamental sampling technique where each member of a population has an equal chance of being included in the sample. This means that every possible sample of the desired size has the same probability of being chosen.

To perform SRS, all individuals in the population must be listed, and a random selection process is used to pick the appropriate number of subjects. This can be done using techniques like lottery methods or random number generators. SRS is prized for its simplicity and the minimized risk of sample bias, ensuring a fair representation of the total population. However, SRS can be impractical or costly when dealing with large populations or hard-to-reach groups.
Stratified Sampling
Stratified sampling is a more complex strategy used when researchers want to ensure representation across key subgroups or strata within a population. In this method, the population is divided into separate groups based on a characteristic known to be a source of variance (e.g., age, income, education level).

After identifying these strata, the researcher performs a simple random sample within each group. This dual-layer approach enhances the statistical efficiency and allows for more targeted analysis of specific strata. It is particularly useful when some segments of a population are small but significant to the study’s objectives. Nevertheless, it requires detailed population information, which is not always available.
Cluster Sampling
Cluster sampling is notably efficient when studying a large, geographically dispersed population. In essence, it capitalizes on natural groupings inherent within the population. Instead of sampling individuals as your primary unit, entire clusters are chosen at random. For instance, if a researcher wanted to sample high school students' opinions on a new educational policy, instead of randomly sampling students across the state (which could be logistically challenging), they might randomly select several schools and survey every student within them.

Clusters should ideally be similar to one another on key dimensions and collectively represent the entire population. This method reduces costs and simplifies sampling logistics, but it comes with an increased risk of sampling error since individuals within a cluster are often more similar to one another than to those in other clusters. Therefore, results should be interpreted with caution, given the potential for decreased precision relative to simple random or stratified sampling.

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Most popular questions from this chapter

Tea and Divergent Creativity In a 2017 study published in the journal Food Quality and Preference, researchers investigated the effect of drinking tea on divergent creativity (Huang et al. 2017 ). Subjects were recruited from a campus Bulletin Board System and were paid a small stipend for their participation. Subjects were randomly assigned to be served either tea or water during the "greeting period" of the experiment. During the greeting period subjects filled out a background questionnaire so they were unaware that beverage was a key component in the study. Subjects were then told to build the most "attractive" building possible in a limited amount of time using a set of blocks. Independent observers then gave each building a creativity score. Read excerpts from the study results and answer the following questions. Results: A general linear model analysis showed that the creativity scores of the block buildings for the tea group (mean \(=6.54\), \(\mathrm{SD}=0.92\) ) were significantly higher than those for the water group (mean \(=6.03, \mathrm{SD}=0.94\) ) after controlling for gender and volume consumed \((p=0.023)\). a. Identify the treatment variable and the response variable. b. Was this a controlled experiment or an observational study? Explain. c. Can you conclude from that drinking tea leads to improved creativity? Why or why not?

Tomato Plants and Fertilizer Suppose you grow tomato plants in a greenhouse and sell the tomatoes by weight, so the amount of money you make depends on plants producing a large total weight of tomatoes. You want to determine which of two fertilizers will produce a heavier harvest of tomatoes, fertilizer \(\mathrm{A}\) or fertilizer \(\mathrm{B}\). There are two distinct regions in the greenhouse: one on the southern side that gets more light and one on the northern side that gets less light. There is room for 20 tomato plants on the southern side and 20 on the northern side. Assume that all the plants are beefsteak tomato plants. a. Identify the treatment and response variables. b. Describe a simple randomized design to test whether fertilizer \(\mathrm{A}\) is better than fertilizer B. c. Describe a blocked design to test which fertilizer produces a greater weight of tomatoes, blocking by southern side and northern side of the greenhouse. Explain why creating blocks based on whether plants are on the southern or northern side makes sense. d. Explain why researchers might prefer a blocked design.

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