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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.Q.7c
Chapter 1, Problem 1.Q.7c

Identify the sampling technique used in each study. Explain your reasoning.
A study on attitudes about smoking is conducted at a college. The students are divided by class (freshman, sophomore, junior, and senior). Then a random sample is selected from each class and interviewed.

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Step 1: Understand the problem. The goal is to identify the sampling technique used in the study. The key details are that students are divided into groups based on class (freshman, sophomore, junior, senior), and then a random sample is taken from each group.
Step 2: Recall the definition of stratified sampling. Stratified sampling is a technique where the population is divided into subgroups (strata) based on a shared characteristic, and then a random sample is taken from each subgroup.
Step 3: Compare the study's method to the definition of stratified sampling. In this study, the population (students) is divided into subgroups (classes), and a random sample is taken from each subgroup. This matches the definition of stratified sampling.
Step 4: Explain why this is not another sampling technique. For example, it is not simple random sampling because the population is divided into subgroups before sampling. It is not cluster sampling because the entire subgroup is not selected; only a random sample from each subgroup is chosen.
Step 5: Conclude that the sampling technique used in this study is stratified sampling, as the population is divided into strata (classes) and random samples are taken from each stratum.

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Key Concepts

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

Stratified Sampling

Stratified sampling is a technique where the population is divided into distinct subgroups, or strata, that share similar characteristics. In the given study, students are categorized by their class year (freshman, sophomore, junior, senior), and a random sample is taken from each class. This method ensures that each subgroup is represented in the sample, which can lead to more accurate and generalizable results.
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Sampling Distribution of Sample Proportion

Random Sampling

Random sampling is a method where each member of a population has an equal chance of being selected for the sample. In the study, after dividing students into classes, a random sample is chosen from each class. This approach minimizes selection bias and helps ensure that the sample reflects the diversity of the entire population, enhancing the validity of the findings.
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Sampling Distribution of Sample Proportion

Sampling Bias

Sampling bias occurs when certain members of a population are systematically more likely to be selected for the sample than others, leading to an unrepresentative sample. In the context of the study, if only one class year was overrepresented or underrepresented, it could skew the results. Understanding this concept is crucial for evaluating the reliability of the study's conclusions about attitudes toward smoking.
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Sampling Distribution of Sample Proportion
Related Practice
Textbook Question

In Exercises 9 and 10, determine whether the study is an observational study or an experiment. Explain.


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Textbook Question

Identify the sampling technique used in each study. Explain your reasoning.

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Determine whether the data are qualitative or quantitative. Explain.

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Textbook Question

Determine whether the study is an observational study or an experiment. Explain.

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Textbook Question

In Exercises 11 and 12, determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set.


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Textbook Question

In Exercises 4 and 5, determine whether the number is a parameter or a statistic. Explain your reasoning.


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