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Chapter 14: Problem 22

Refer to the following story: The 1250 students at Eureka High School are having an election for Homecoming King. The candidates are Tomlinson (captain of the football team), Garcia (class president), and Marsalis (member of the marching band). At the football game a week before the election, a pre- election poll was taken of students as they entered the stadium gates. Of the students who attended the game, 203 planned to vote for Tomlinson, 42 planned to vote for Garcia, and 105 planned to vote for Marsalis. Name the sampling method used for this survey.

Short Answer

Expert verified
The sampling method used for the survey in this exercise is Convenience Sampling.

Step by step solution

01

Identify the sampling

The students were selected for the survey as they entered the stadium gates for a football game. This is a specific event, suggesting that the sample was not randomly selected from the entire student body of 1250 students at Eureka High School.
02

Define the Sampling Method

The method used here is a type of non-probability sampling called convenience sampling. \n\nNon-probability sampling is a sampling technique where the samples are gathered in a process that does not give all the individuals in the population equal chances of being selected. \n\nConvenience sampling is a type of non-probability sampling where the samples are selected because they are convenient. This sampling method is based on the judgment of the researcher and is often used when access to a total population is difficult.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Convenience Sampling
Convenience sampling is one of the simplest methods used in data collection. In this approach, samples are picked based on ease of access rather than a structured process. In the case of our election scenario at Eureka High School, students were surveyed as they entered a football game. This location was chosen purely for its accessibility and the fact that a large group of potential respondents was already gathered.

Some key characteristics of convenience sampling include:
  • Speed and ease of execution. You can quickly gather data without complex planning.
  • Lack of representative representation. The sample might not reflect the whole population fairly.
  • Subject to bias. Since not all potential participants have an equal chance of being chosen, the results may be skewed.
Despite its drawbacks, it is widely used in preliminary research where a general view is needed quickly without a rigorous statistical framework.
Non-Probability Sampling
Non-probability sampling occurs when not all individuals in a population have an equal chance of being selected to participate. Convenience sampling is a subset of this broader category. In non-probability sampling, the focus is less on statistical significance and more on exploratory research.

There are several types of non-probability sampling:
  • Judgmental Sampling: The researcher uses their expertise to select the sample, which they believe will be most representative.
  • Snowball Sampling: Current study subjects recruit future subjects from among their acquaintances, forming a chain-like sample.
  • Quota Sampling: A non-random sample is selected according to some fixed quota.
In conjunction with convenience sampling used at the game, the alignment with non-probability sampling emphasizes that only certain students had the opportunity to be surveyed, potentially missing voices that might have impacted the overall results.
Statistical Surveys
Statistical surveys are used to collect data from a predefined group of respondents to gain information and insights. Surveys, whether they employ probability or non-probability methods like convenience sampling, are pivotal in gathering data to draw conclusions about larger populations.

Several stages are involved in conducting successful statistical surveys:
  • Designing the Questionnaire: Ensure questions are clear and unbiased to avoid influencing answers.
  • Selecting a Sampling Method: Determine whether to use probability (random) sampling or non-probability sampling methods.
  • Collecting the Data: This involves reaching out to the selected sample set and gathering their responses.
  • Analyzing the Data: Data must be interpreted correctly to derive meaningful insights or conclusions.
The pre-election poll taken at Eureka High School served as a simple example of a statistical survey, although it leaned towards convenience sampling rather than a fully randomized statistical method. Understanding these basic tenets helps illuminate the broader implication of capturing and analyzing survey data.

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Most popular questions from this chapter

Refer to the following story: The manufacturer of a new vitamin (vitamin \(X\) ) decides to sponsor a study to determine the vitamin's effectiveness in curing the common cold. Five hundred college students having a cold were recruited from colleges in the San Diego area and were paid to participate as subjects in this study. The subjects were each given two tablets of vitamin \(X\) a day. Based on information provided by the subjects themselves, 457 of the 500 subjects were cured of their colds within 3 days. (The average number of days a cold lasts is 4.87 days.) As a result of this study, the manufacturer launched an advertising campaign based on the claim that "vitamin \(X\) is more than \(90 \%\) effective in curing the common cold." List four different problems with the study that indicate poor design.

Refer to the following story: The 1250 students at Eureka High School are having an election for Homecoming King. The candidates are Tomlinson (captain of the football team), Garcia (class president), and Marsalis (member of the marching band). At the football game a week before the election, a pre- election poll was taken of students as they entered the stadium gates. Of the students who attended the game, 203 planned to vote for Tomlinson, 42 planned to vote for Garcia, and 105 planned to vote for Marsalis. (a) Give the sample statistics estimating the percentage of the vote going to each candidate. (b) A week after this survey, Garcia was elected Homecoming King with \(51 \%\) of the vote, Marsalis got \(30 \%\) of the vote, and Tomlinson came in last with \(19 \%\) of the vote. Find the sampling errors in the survey expressed as percentages.

A large jar contains an unknown number of red gumballs and 150 green gumballs. As part of a seventh-grade class project the teacher asks Carlos to estimate the total number of gumballs in the jar using a sample. Carlos draws a sample of 50 gumballs, of which 19 are red and 31 are green. Use Carlos' sample to estimate the number of gumballs in the jar.

One implicit assumption when using the capture-recapture method to estimate the size of a population is that the capture process is truly random, with all individuals having the same likelihood of being captured. Sometimes that is not true, and some populations have a large number of individuals that are "trap-happy" individuals (more prone to capture than others, more likely to take the bait, less cagey, slower, dumber, etc.). If that were the case, would the capture-recapture method be likely to underestimate or overestimate the size of the population? Explain your answer.

Refer to a study conducted between 2008 and 2010 on the effectiveness of saw palmetto fruit extracts at treating lower urinary tract symptoms in men with prostate enlargement. (Saw palmetto is a widely used over-the-counter supplement for treating urinary tract symptoms.) In the study, 369 men aged 45 years or older were randomly divided into a group taking a daily placebo and a group taking saw palmetto. Participants were nonpaid volunteers recruited at 11 North American sites. All had moderately impaired urinary flow. Because the saw palmetto extract has a mild odor, the doses were administered using gelcaps to eliminate the odor. In an analysis of the 306 men who completed the 72 -week trial, both groups had similar small improvements in mean symptom scores, but saw palmetto conferred no benefit over placebo on symptom scores or on any secondary outcomes. (a) Describe the treatment group in the study. (b) Explain why the experimenters took the trouble to cover the mild odor of saw palmetto to the point of packaging the doses in the form of gelcaps. (c) Was this study a blind, randomized, controlled placebo study? Explain.
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