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Chapter 1: Problem 7

Use the following information to answer the next four exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed. The sampling method was a. simple random b. systematic c. stratified d. cluster

Short Answer

Expert verified
The sampling method is systematic (b).

Step by step solution

01

Identify Key Aspects of the Method

In this sampling method, the first house was chosen randomly, and then residents were chosen from every eighth house after that. This pattern indicates a systematic approach was used to collect data.
02

Understand Systematic Sampling

Systematic sampling is a type of probability sampling method where elements from a larger population are selected after a random starting point at a regular interval. This method is characterized by its regular and periodic selection.
03

Consider the Definitions of Other Sampling Methods

- Simple random sampling involves selecting participants completely at random without any pattern. - Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each one. - Cluster sampling involves selecting entire groups or clusters from the population. None of these match the description of the method used.
04

Draw a Conclusion Based on Analysis

By comparing the provided sampling method to the different definitions, we can confirm that the described method aligns with systematic sampling because of the regular interval used after a random start.

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Key Concepts

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

Systematic Sampling
Systematic sampling is a widely used method of probability sampling. It involves selecting survey or data collection participants at a regular interval after a randomized starting point. For example, in the exercise, the study started with a randomly chosen house, then every eighth house was selected thereafter.

This technique ensures that the sample is spread evenly over a population, which helps in reducing potential biases that might arise from selecting participants too close together either geographically or chronologically.

Key characteristics of systematic sampling include:
  • Random start: The process begins with selecting an initial participant through a random mechanism to ensure every unit has an equal chance to be the starting point.
  • Fixed interval: After the initial random choice, all subsequent selections are made at regular intervals, such as every eighth house, as in our example.
  • Simplicity and efficiency: This method is simple to implement and efficient for large populations.
Overall, systematic sampling is beneficial when you know your population is homogenous, and you expect minimal variation between successive units.
Probability Sampling
Probability sampling is a method used to select samples from a population where each member has a known, non-zero chance of being selected. This characteristic makes it a fair method and allows statistical conclusions about the entire population.

Different forms of probability sampling include:
  • Simple random sampling: Every member of the population has an equal chance of being selected. It's akin to drawing names out of a hat.
  • Systematic sampling: Involves selecting every nth member after a random start, as explained previously.
  • Stratified sampling: Divides the population into subgroups and samples from each subgroup, ensuring representation across key variables.
  • Cluster sampling: The population is divided into clusters, and a whole cluster is randomly selected.
By employing probability sampling, researchers can make valid inferences about a population since the sample is likely to reflect the population's diversity.
Data Collection Techniques
Data collection techniques include various methods for gathering information to analyze it effectively. They are critical in research, influencing the results' validity and reliability.

The choice of data collection methods varies depending on the research goal and population characteristics. Some techniques are:
  • Surveys and Questionnaires: These are often used for obtaining quantitative data and can be distributed to large samples efficiently.
  • Interviews: Provide deeper, qualitative insights but may be more time-consuming and require trained personnel to administer.
  • Observations: Involving watching subjects without interference to capture natural behaviors.
In the given exercise, interviews were conducted at every eighth household. This choice aligns with a practical and feasible approach when direct interaction is possible and desired to collect detailed information. Each technique has its strengths and limitations, but choosing the right one is key to the study's success.

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Most popular questions from this chapter

Discuss potential violations of the rule requiring informed consent. a. Inmates in a correctional facility are offered good behavior credit in return for participation in a study. b. A research study is designed to investigate a new children鈥檚 allergy medication. c. Participants in a study are told that the new medication being tested is highly promising, but they are not told that only a small portion of participants will receive the new medication. Others will receive placebo treatments and traditional treatments.

In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards. a. Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time. b. What effect does the low response rate have on the reliability of the sample? c. Are these problems examples of sampling error or non sampling error? d. During the same year, George Gallup conducted his own poll of 30,000 prospective voters. His researchers used a method they called "quota sampling" to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

Use the following information to answer the next seven exercises: Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected. Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34 Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29 Suppose that the second researcher conducted his survey by choosing 40 patients he knew. What sampling method would that researcher have used? What concerns would you have about this data set, based upon the data collection method?

Use the following data to answer the next five exercises: Two researchers are gathering data on hours of video games played by school-aged children and young adults. They each randomly sample different groups of 150 students from the same school. They collect the following data. $$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Hours Played per week } & {\text { Frequency }} & {\text { Relative Frequency }} & {\text { Cumulative Relative Frequency }} \\ \hline 0-2 & {26} & {0.17} & {0.17} \\ \hline 2-4 & {30} & {0.20} & {0.37} \\ \hline 4-6 & {49} & {0.33} & {0.70} \\ \hline 6-8 & {25} & {0.17} & {0.87} \\ \hline 8-10 & {12} & {0.8} & {0.95} \\ \hline 10-12 & {8} & {0.05} & {1} \\ \hline\end{array}$$ Table 1.29 Researcher A $$\begin{array}{|l|l|l|l|}\hline \text { Hours Played per week } & {\text { Frequency }} & {\text { Relative Frequency }} & {\text { Cumulative Relative Frequency }} \\ \hline 0-2 & {0.48} & {0.32} & {0.32} \\ \hline 2-4 & {51} & {0.34} & {0.66} \\ \hline 4-6 & {24} & {0.16} & {0.82} \\ \hline 6-8 & {12} & {0.08} & {0.90} \\ \hline 8-10 & {11} & {0.07} & {0.97} \\ \hline 10-12 & {4} & {0.03} & {1} \\ \hline \end{array}$$ Table 1.30 Researcher B Researcher A concludes that most students play video games between four and six hours each week. Researcher B concludes that most students play video games between two and four hours each week. Who is correct?

The Gallup-Health ways Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below. Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous. a. Do you have any health problems that prevent you from doing any of the things people your age can normally do? b. During the past 30 days, for about how many days did poor health keep you from doing your usual activities? c. In the last seven days, on how many days did you exercise for 30 minutes or more? d. Do you have health insurance coverage?
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