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Ch. 1 - Introduction to Statistics
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 1 - Introduction to StatisticsProblem 1.RE.7e
Chapter 1, Problem 1.RE.7e

State Populations Currently, California has the largest population with 39,776,830 residents, and Wyoming has the smallest population with 573,520 residents.


e. If we randomly select two states and survey all of their adult residents, what type of sample is obtained? (random, systematic, convenience, stratified, cluster)

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1
Understand the different types of sampling methods: Random sampling involves selecting individuals purely by chance, systematic sampling involves selecting every nth individual, convenience sampling involves selecting individuals who are easiest to reach, stratified sampling involves dividing the population into subgroups and sampling from each, and cluster sampling involves dividing the population into clusters and randomly selecting entire clusters.
Identify the key characteristics of the problem: The problem involves selecting two states and surveying all of their adult residents.
Consider the definition of cluster sampling: In cluster sampling, the population is divided into clusters (in this case, states), and entire clusters are selected randomly. All individuals within the selected clusters are then surveyed.
Analyze the problem in the context of cluster sampling: Since the problem involves selecting entire states (clusters) and surveying all adult residents within those states, it aligns with the definition of cluster sampling.
Conclude that the type of sample obtained is a cluster sample, as the selection process involves choosing entire clusters (states) and surveying all individuals within those clusters.

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Key Concepts

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

Sampling Methods

Sampling methods are techniques used to select a subset of individuals from a population to estimate characteristics of the whole population. Common methods include random, systematic, convenience, stratified, and cluster sampling, each with unique procedures and applications. Understanding these methods helps in choosing the appropriate technique for data collection based on the research objective.
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Sampling Distribution of Sample Proportion

Cluster Sampling

Cluster sampling involves dividing the population into distinct groups, or clusters, and then randomly selecting entire clusters for study. This method is efficient when dealing with large, geographically dispersed populations, as it reduces travel and administrative costs. In the context of the question, selecting two states and surveying all their residents exemplifies cluster sampling.
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Stratified Sampling

Stratified sampling involves dividing the population into homogeneous subgroups, or strata, and then randomly sampling from each stratum. This ensures representation across key characteristics, improving the accuracy and reliability of results. Unlike cluster sampling, stratified sampling requires sampling from each subgroup, not entire groups, making it distinct in its approach to achieving representativeness.
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Related Practice
Textbook Question

Paying for First Dates USA Today posted this question on the electronic version of its newspaper: “Should guys pay for the first date?” Of the 1148 subjects who decided to respond, 85% of them said “yes.”


a. What is wrong with this survey?

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Textbook Question

Divorces and Margarine One study showed that there is a very high correlation between the divorce rate in Maine and per capita consumption of margarine in the United States. Can we conclude that either one of those two variables is the cause of the other?

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Textbook Question

Reported Versus Measured In a survey of 1046 adults conducted by Bradley Corporation, subjects were asked how often they wash their hands when using a public restroom, and 70% of the respondents said “always.”


a) Identify the sample and the population.

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Textbook Question

Sampling For each of the following, identify the term that best describes the type of sample: systematic, convenience, stratified, cluster, or simple random sample.


b. To test for a gender difference in the way that men and women make online purchases, Gallup surveys 500 randomly selected men and 500 randomly selected women.

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Textbook Question

Simple Random Sample vs. Random Sample Refer to the definition of simple random sample here and its accompanying definition of random sample enclosed within parentheses. Determine whether each of the following is a simple random sample and a random sample.


a. In Major League Baseball, there are 30 teams, each with an active roster of 25 players. The names of the teams are printed on 30 separate index cards, the cards are shuffled, and one card is drawn. The sample consists of the 25 players on the active roster of the selected team.

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Textbook Question

Sampling Method Assume that the population consists of all students currently in your statistics class. Describe how to obtain a sample of six students so that the result is a sample of the given type.


a. Simple random sample

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