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Notes and Solutions for Mathematical Applications with Statistics, 7th Ed. by Wackerly, Mendenhall, and Scheaffer

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Section 1.1 Introduction

Numerous definitions of statistics are given, and each description implies that data are collected, with inference as the objective. Each requires selecting a subset of a large collection of data, either existent or conceptual, in order to infer the characteristics of the complete set. All the authors imply that statistics is a theory of information, with inference making as its objective.
The large body of data that is the target of our interest is called the population, and the subset selected from it is a sample… Information useful in inferring some characteristic of a population (either existent or conceptual) is purchased in a specified quantity and results in an inference (estimation or decision) with an associated degree of goodness…

Exercises Exercises

1.1.

For each of the following situations, identify the population of interest, the inferential objective, and how you might go about collecting a sample.
(a)
The National Highway Safety Council wants to estimate the proportion of automobile tires with unsafe tread among all tires manufactured by a specific company during the current production year.
Solution.
The population of interest is all tires manufactured by a specific company during the current production year, the inferential objective is to estimate the proportion of tires with unsafe tread among the population, and a sample could be collected by taking measurements at the specific tire manufacturer.
(b)
A political scientist wants to determine whether a majority of adult residents of a state favor a unicameral legislature.
Solution.
The population of interest is adult residents of a state, the inferential objective is to determine how high the proportion of adult residents in the state who favor a unicameral legislature is, and a sample could be collected by polling adult residents in the state.
(c)
A medical scientist wants to estimate the average length of time until the recurrence of a certain disease.
Solution.
The population of interest is people who have had a certain disease, the inferential objective is estimating the average length of time until the disease recurs in someone who has had it before, and a sample could be collected by consulting a database of medical records for people who have experienced the disease.
(d)
An electrical engineer wants to determine whether the average length of life of transistors of a certain type is greater than 500 hours.
Solution.
The population of interest is transistors of a certain type, the inferential objective is determining whether that type of transistor has an average lifespan of more than 500 hours, and a sample could be collected by by measuring how long each transistor in a sample of transistors of that type lasts for.
(e)
A university researcher wants to estimate the proportion of U.S. citizens from "Generation X" who are interested in starting their own businesses.
Solution.
The population of interest is U.S. citizens from Generation X, the inferential objective is to determine the proportion of U.S. citzen Gen X-ers who are interesting in starting their own businesses, and a sample could be collected by polling U.S. citizen Gen X-ers.
(f)
For more than a century, normal body temperature for humans has been accepted to be 98.6° Fahrenheit. Is it really? Researchers want to estimate the average temperature of healthy adults in the United States.
Solution.
The population of interest is healthy adults in the United States, the inferential objective is estimating the average temperature of health adults in the United States, and a sample could be collected by measuring the temperature of a sample of healthy adults in the United States.
(g)
A city engineer wants to estimate the average weekly water consumption for single-family dwelling units in the city.
Solution.
The population of interest is single-family dwelling units in the city, the inferential objective is to estimate the average weekly water consumption for single-family dwelling units in the city, and a sample could be collected by measuring the water consumption of a sample of single-family dwelling units in the city.
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