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Chapter 1: Problem 21

Identify the type of sampling used. A statistics instructor with a large number of students attempts to reduce time spent grading by only grading a portion of assigned homework problems. He randomly selects one of the first four problems in the assignment and then grades that problem and every fourth problem thereafter.

Short Answer

Expert verified
Systematic Sampling

Step by step solution

01

Understand the Problem

The instructor has numerous students and wants to minimize grading time by only grading a portion of the assigned homework. The instructor's method involves randomly selecting one of the first four problems and then continuing to grade every fourth problem.
02

Identify the Sampling Method

Consider the method used: starting with a random problem from the first four and then selecting every fourth problem after that.
03

Compare with Sampling Methods

There are various types of sampling methods: simple random sampling, stratified sampling, cluster sampling, systematic sampling, etc. Here, the key aspect is the fixed periodic interval (every fourth problem), which hints towards a specific pattern.
04

Conclusion

Since the instructor randomly selects one initial problem and continues grading every fourth problem, this method fits the characteristics of systematic sampling.

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Key Concepts

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

Sampling Methods
Sampling methods are techniques used to select a portion of a population to represent the whole. There are several different ways to do this, each with its own strengths and weaknesses. Here are a few common sampling methods:

  • Simple Random Sampling: Every member of the population has an equal chance of being selected. This is the most straightforward form of sampling.
  • Stratified Sampling: The population is divided into smaller groups, or strata, based on a shared characteristic, and then samples are taken from each stratum.
  • Cluster Sampling: The population is divided into clusters, often based on geography or other arbitrary means. A random sample of clusters is chosen, and then all members of those clusters are surveyed.
  • Systematic Sampling: A starting point is chosen at random, and samples are taken at regular intervals from there. This is particularly useful when dealing with a large population where random sampling might be impractical.
Each method is suitable for different types of research and can be chosen based on the specific goals, nature of the population, and resources available.
Systematic Sampling
Systematic sampling, the method used by the instructor in the exercise, involves selecting elements from an ordered population using a fixed, periodic interval. Here's how it works:

  • Select a Starting Point: This point is chosen at random from the initial part of the population. For example, the instructor chose one of the first four problems randomly.
  • Determine the Interval: A fixed interval is set for the selection process. The instructor chose every fourth problem after the initial random selection.
  • Proceed Systematically: Continue selecting elements at the set interval throughout the population. This ensures a degree of randomness while being systematic and easy to implement.
Systematic sampling is efficient and ensures that the sample is spread out across the entire population. However, it might introduce a bias if there鈥檚 a hidden pattern in the population that aligns with the sampling interval.
Statistics Education
Understanding different sampling methods is a crucial part of statistics education. It helps students grasp how data can be gathered and ensures that the samples are representative of the population. Here鈥檚 why learning about sampling is essential:

  • Foundation for Data Analysis: Sampling is the first step in data analysis. Knowing how to collect a sample correctly ensures that the results of the analysis are valid.
  • Reducing Bias: Different methods help reduce biases that can distort the results of a study. Understanding these methods allows students to choose the most appropriate one for their research.
  • Practical Application: Statistics education often involves practical exercises that mimic real-world scenarios. Grasping the concept of sampling helps students apply their learning to situations they might encounter in their careers.
  • Efficient Resource Use: Learning about systematic sampling, for example, can teach students how to save time and resources while still obtaining reliable data.
By thoroughly understanding these concepts, students can design better studies and make more informed decisions based on the data they collect.

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Most popular questions from this chapter

A local youth advisory committee is comprised of 18 youths and 6 adults. The committee needs to select 2 adults and 4 youths to meet with the mayor to discuss renovations of the community center. The members of the committee are: Youth: Patrick, Elise, Shawn, Lauren, Sandra, Josh, Erin, Payton, Michelle, Chad, Katy, Amanda, Jim, Janice, Jeff, Amy, Logan, Steve Adults: Harold, Kerry, Keith, Greg, Marcie, Debbie Obtain a stratified random sample of 4 youths and 2 adults.

A marketing executive for Coca-Cola Inc., wants to identify television shows that people in the Boston area who typically drink Coke are watching. The executive has a list of all households in the Boston area. Design a sampling method to obtain the individuals in the sample. Be sure to support your choice.

Determine whether the quantitative variable is discrete or continuous. Length of a country song

For the studies in Problems \(45-50,\) (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study. The Mozart Effect Researchers at the University of California, Irvine, wished to determine whether "music cognition and cognitions pertaining to abstract operations such as mathematical or spatial reasoning" were related. To test the research question, 36 college students listened to Mozart's Sonata for Two Pianos in D Major, K488, for 10 minutes and then took a spatial reasoning test using the Stanford-Binet intelligence scale. The same students also took the test after sitting in a room for 10 minutes in complete silence. Whether the student experienced Mozart first or silence first was randomly determined. The average score on the test following the Mozart piece was \(119,\) while the average test score following the silence was 110. The researchers concluded that subjects performed better on abstract and spatial reasoning tests after listening to Mozart. (Source: "Music and Spatial Performance," Frances H. Rauscher et al.; Nature 365,14 October 1993: 611 )

Determine whether the quantitative variable is discrete or continuous. At rest pulse rate of a 20 -year-old college student
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