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Ch. 1 - Introduction to Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 1 - Introduction to StatisticsProblem 1.r.29
Chapter 1, Problem 1.r.29

You want to know the favorite spring break destination among 15,000 students at a university. Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain your reasoning.

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Step 1: Understand the problem. The goal is to determine the favorite spring break destination among 15,000 students at a university. A census involves collecting data from every individual in the population, while sampling involves collecting data from a subset of the population.
Step 2: Evaluate the feasibility of a census. A census would require surveying all 15,000 students, which is likely to be time-consuming, expensive, and logistically challenging. Therefore, a sampling method is more practical in this case.
Step 3: Choose an appropriate sampling technique. Common sampling techniques include simple random sampling, stratified sampling, cluster sampling, and systematic sampling. The choice depends on the population's characteristics and the resources available.
Step 4: Justify the sampling technique. For example, if the student population is diverse in terms of demographics or preferences, stratified sampling might be appropriate. This involves dividing the population into strata (e.g., by year of study or major) and sampling proportionally from each stratum to ensure representation.
Step 5: Explain the reasoning. Sampling is chosen because it is more efficient and cost-effective than a census. The specific sampling technique ensures that the sample is representative of the entire student population, allowing for accurate conclusions about their favorite spring break destinations.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Census vs. Sampling

A census involves collecting data from every member of a population, providing complete information but often requiring significant time and resources. In contrast, sampling involves selecting a subset of the population to infer characteristics about the whole. For large populations, like 15,000 students, sampling is typically more practical and cost-effective.
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Sampling Distribution of Sample Proportion

Sampling Techniques

Sampling techniques are methods used to select individuals from a population for a study. Common techniques include random sampling, where every individual has an equal chance of selection, and stratified sampling, which involves dividing the population into subgroups and sampling from each. The choice of technique affects the representativeness and reliability of the results.
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Sampling Distribution of Sample Proportion

Representativeness

Representativeness refers to how well a sample reflects the characteristics of the larger population. A representative sample ensures that the findings can be generalized to the entire population. Factors such as sample size and selection method play crucial roles in achieving representativeness, which is essential for drawing valid conclusions about students' favorite spring break destinations.
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Textbook Question

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