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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.5a
Chapter 1, Problem 1.RE.5a

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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1
Understand the different types of sampling methods: Systematic, Convenience, Stratified, Cluster, and Simple Random Sample.
Systematic sampling involves selecting every nth item from a list or production line. In this case, every 500th pill is selected.
Convenience sampling involves selecting items that are easy to access or obtain, which is not applicable here.
Stratified sampling involves dividing the population into subgroups and then taking a sample from each subgroup, which is not the method used here.
Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters, which is not the method used here.
Simple random sampling involves selecting items entirely by chance, without a specific pattern, which is not the method used here.
Based on the description, the sampling method used is systematic sampling, as every 500th pill is selected for testing.

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Key Concepts

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

Systematic Sampling

Systematic sampling involves selecting elements from an ordered sampling frame at regular intervals. In the given question, every 500th Lipitor pill is chosen for testing, which exemplifies systematic sampling. This method is efficient and ensures a spread across the entire production process, reducing the risk of bias.
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Sampling Distribution of Sample Proportion

Sampling Frame

A sampling frame is a list or database from which a sample is drawn. It includes all the elements of the population that can be sampled. In the context of the question, the sampling frame would be the entire batch of Lipitor pills produced, from which every 500th pill is selected for quality control testing.
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Sampling Distribution of Sample Proportion

Quality Control

Quality control refers to the process of ensuring products meet certain standards and specifications. In the question, testing every 500th Lipitor pill for the correct dosage of atorvastatin is a quality control measure. This systematic approach helps maintain product consistency and safety, ensuring that each pill meets the required pharmaceutical standards.
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State Populations Currently, California has the largest population with 39,776,830 residents, and Wyoming has the smallest population with 573,520 residents.


a. Are the population sizes of the different states discrete or continuous?

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c. Does the survey constitute an experiment or an observational study?

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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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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

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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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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