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

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


d. If we randomly select 50 full-time workers in each of the 50 states, 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 sample described in the problem: We are selecting 50 full-time workers from each of the 50 states.
Recognize that the sample involves dividing the population (all full-time workers in the U.S.) into subgroups (the 50 states).
Note that from each subgroup (state), a sample of 50 full-time workers is selected.
Determine that this method of sampling, where the population is divided into subgroups and samples are taken from each subgroup, is known as stratified sampling.

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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 its own advantages and applications depending on the research goals and population structure.
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Sampling Distribution of Sample Proportion

Stratified Sampling

Stratified sampling involves dividing a population into distinct subgroups, or strata, that share similar characteristics, and then randomly selecting samples from each stratum. This method ensures representation from all subgroups, making it useful when the population has diverse segments that need to be proportionally represented in the sample.
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Sampling Distribution of Sample Proportion

Cluster Sampling

Cluster sampling involves dividing the population into clusters, usually based on geographical or natural groupings, and then randomly selecting entire clusters for study. This method is efficient for large populations spread over wide areas, as it reduces travel and administrative costs by focusing on specific clusters rather than individuals.
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Related Practice
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.


a. As Lipitor pills are being manufactured, a quality control plan is to select every 500th pill and test it to confirm that it contains 80 mg of atorvastatin.

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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.”


b. Is the value of 85% a statistic or a parameter?

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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

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

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


b. What is the level of measurement for the numbers of residents in the different states? (nominal, ordinal, interval, ratio)

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