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Chapter 1: Problem 2

Define simple random sampling.

Short Answer

Expert verified
Simple random sampling gives each population member an equal chance of selection, ensuring unbiased representation.

Step by step solution

01

Definition of Simple Random Sampling

Simple random sampling is a fundamental sampling method where each member of the population has an equal chance of being selected. This ensures that the sample represents the population without bias.
02

Importance of Equal Probability

In simple random sampling, equal probability means that all possible samples of a given size have the same chance of being chosen. This helps in obtaining unbiased statistical estimates of the population parameters.
03

Method of Selection

Typically, simple random sampling can be achieved through techniques such as using a random number generator, drawing names out of a hat, or using random number tables. These methods ensure that the selection process is purely by chance.

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Key Concepts

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

Equal Probability Selection
In simple random sampling, every member of the population has an equal chance of being chosen. This might sound simple, but it is a crucial concept. Without equal probability, some members might be more likely to be picked, which could lead to biased results. Think of it like a fair game of lottery: each ticket has the same chance of winning.

Here鈥檚 why it matters:
  • Fair Representation: It ensures that no particular group within the population is over or under-represented.
  • Reduces Bias: Equal probability helps in minimizing selection bias, which can distort the findings.
Always remember, if each member does not have an equal chance, it鈥檚 not a simple random sample.
Unbiased Statistical Estimates
One of the main benefits of simple random sampling is obtaining unbiased statistical estimates. But what does that mean? Let鈥檚 break it down. An unbiased estimate means that the sample accurately represents the population, so the results we get from the sample are close to what we would get if we studied the whole population.

Advantages of Unbiased Estimates:
  • Accuracy: It provides an accurate reflection of the population parameters like mean or variance.

  • Reliability: Since the sample is unbiased, we can trust the data to make decisions or predictions about the population.
For example, if you were trying to estimate the average height of students in a school, a simple random sample would give you a height that鈥檚 closer to the actual average height if you measured every student.
Random Selection Methods
There are several methods to ensure random selection in simple random sampling:

  • Random Number Generators: These are computer algorithms that can generate random numbers to select members from the population.

  • Drawing Names Out of a Hat: A more manual method, but equally effective, involves writing each person鈥檚 name on a piece of paper, mixing them well, and drawing without looking.

  • Random Number Tables: These tables are pre-generated sequences of random numbers that can also be used for selection.
No matter which method you choose, the key is to ensure randomness. This maintains the equal probability principle and helps achieve unbiased results in your sample.

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Most popular questions from this chapter

A research objective is presented. For each, identify the population and sample in the study. A community college notices that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks how many hours per week each works.

True or False: Generally, the goal of an experiment is to determine the effect that treatments will have on the response variable.

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