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Chapter 1: Problem 71

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is a. cluster sampling b. stratified sampling c. simple random sampling d. convenience sampling

Short Answer

Expert verified
Stratified Sampling

Step by step solution

01

Understand the Question

The exercise asks us to identify the sampling technique used when selecting five students from each class at a community college. This involves recognizing patterns from the context.
02

Define Key Terms

Familiarize yourself with the definitions of the given sampling methods: Cluster Sampling (choosing random groups instead of individuals), Stratified Sampling (dividing the population into strata and selecting samples from each), Simple Random Sampling (randomly selecting individuals), and Convenience Sampling (selecting samples from readily available groups).
03

Analyze the Sampling Method

In this exercise, the instructor selects five students from each math class, which means the population is divided into groups or 'strata' based on classes, and a sample is selected from each group.
04

Identify the Correct Sampling Technique

Recognizing that each class represents a 'stratum,' and the instructor takes a sample from each, fits the definition of 'Stratified Sampling'.

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Key Concepts

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

Understanding Sampling Methods
Sampling methods are crucial in statistical analysis as they help researchers collect data systematically and ensure it is representative of the population. There are several different types of sampling methods:
  • Stratified Sampling: This method involves dividing the population into separate groups, known as 'strata,' based on shared characteristics (like class, age, or income level). Samples are then randomly selected from each stratum. This technique ensures that each subgroup is properly represented in the overall sample, which helps improve the precision and credibility of the results.
  • Cluster Sampling: Instead of sampling individuals, entire groups or 'clusters' are chosen randomly. This is often used when the population is spread out over a large area, making it difficult to sample each individual.
  • Simple Random Sampling: Every individual in the population has an equal chance of being selected. This is the simplest way to select a sample but can be less efficient if the population is large and diverse.
  • Convenience Sampling: This involves selecting samples that are easiest to reach or available. It is not usually recommended for rigorous research due to its high risk of bias.
Understanding these methods helps in selecting the most appropriate one for the study goals, ensuring accuracy and reliability in the conclusions drawn from the data.
The Role of Statistical Analysis
Statistical analysis is a key component in interpreting data and making informed decisions. It involves various processes:
  • Data Collection: First step involves gathering information through methods like surveys, observations, or experiments.
  • Data Organization: Collected data is then organized systematically, often using tables or graphs for easy analysis.
  • Data Analysis: This step employs statistical methods to identify patterns or trends from the data. Techniques might include measures of central tendency (like mean or median), variability (like variance or standard deviation), and testing hypotheses.
  • Data Interpretation: Finally, insights and conclusions are drawn from the analysis, helping researchers answer key questions or test specific hypotheses.
In educational settings, statistical analysis is especially important to understand and improve teaching methods, learning outcomes, and student performance. It allows educators to identify effective strategies and optimize their approaches for different groups of students.
Educational Statistics in Practice
Educational statistics is a specialized area focusing on the application of statistical methods within education systems. It plays a crucial role in informing and shaping educational policies and practices. Here's how:
  • Assessing Student Performance: By analyzing test scores and other forms of student assessments, educators can identify areas where students excel or need improvement.
  • Evaluating Teaching Methods: Statistical analysis helps determine the effectiveness of different teaching strategies, aiding in the adoption of best practices.
  • Policy Making: Data-driven insights from educational statistics guide policy decisions, ensuring they are aligned with student needs and educational goals.
  • Resource Allocation: Schools and districts use statistical data to allocate resources efficiently, making sure support is directed where it's most needed.
Overall, educational statistics support the development of a more effective and equitable education system, fostering an environment where every student has the opportunity to succeed.

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Most popular questions from this chapter

List some practical difficulties involved in getting accurate results from a telephone survey.

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation. Use key terms from this module to describe the design of this experiment.

A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter. What is the population she is interested in? a. all Lake Tahoe Community College students b. all Lake Tahoe Community College English students c. all Lake Tahoe Community College students in her classes d. all Lake Tahoe Community College math students

Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience). A group of test subjects is divided into twelve groups; then four of the groups are chosen at random.

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 Give a reason why the data may differ.
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