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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

To determine if topiramate is a safe and effective treatment for alcohol dependence, researchers conducted a 14 -week trial of 371 men and women aged 18 to 65 years diagnosed with alcohol dependence. In this double-blind, randomized, placebo-controlled experiment, subjects were randomly given either 300 milligrams (mg) of topiramate (183 subjects) or a placebo (188 subjects) daily, along with a weekly compliance enhancement intervention. The variable used to determine the effectiveness of the treatment was self-reported percentage of heavy drinking days. Results indicated that topiramate was more effective than placebo at reducing the percentage of heavy drinking days. The researchers concluded that topiramate is a promising treatment for alcohol dependence. (a) What does it mean for the experiment to be placebocontrolled? (b) What does it mean for the experiment to be double-blind? Why do you think it is necessary for the experiment to be double-blind? (c) What does it mean for the experiment to be randomized? (d) What is the population for which this study applies? What is the sample? (e) What are the treatments? (f) What is the response variable?

Magnum, LLC, is a web page design firm that has two designs for an online hardware store. To determine which is the more effective design, Magnum uses one page in the Denver area and a second page in the Miami area. For each visit, Magnum records the amount of time visiting the site and the amount spent by the visitor. (a) What is the explanatory variable in this study? Is it qualitative or quantitative? (b) What are the two response variables? For each response variable, state whether it is qualitative or quantitative. (c) Explain how confounding might be an issue with this study.

Does alerting shoppers at a grocery store regarding the healthiness (or lack thereof) of energydense snack foods change the shopping habits of overweight individuals? To answer this question, researchers randomly gave 42 overweight shoppers a recipe flyer that either contained health information or did not contain the health information. This type of intervention is referred to as priming. To determine purchases. the receipts of the participants were reviewed. Results of the study found that shoppers primed with the health- and diet-related words on the recipe bought significantly (almost \(75 \%\) ) fewer unhealthy snacks than those without the primes. (a) What is the research objective? (b) Who are the subjects? (c) Explain why blinding is not possible in this study. (d) What is the explanatory variable in the study. (e) The response variable was number of unhealthy snacks purchased. Is this quantitative or qualitative? (f) Another factor in the study was weight status (normal weight vs overweight). Suppose all the normal weight subjects were given the flyer with the prime and overweight subjects were given the flyer without the prime. Explain how confounding would play a role in the study.

In Problems 11-22, identify the type of sampling used. A farmer divides his orchard into 50 subsections, randomly selects \(4,\) and samples all the trees within the 4 subsections to approximate the yield of his orchard.

In Problems 11-22, identify the type of sampling used. To obtain students' opinions about proposed changes to course registration procedures, the administration of a small college asked for faculty volunteers who were willing to administer a survey in one of their classes. Twenty-three faculty members volunteered. Each faculty member gave the survey to all the students in one course of their choosing. Would this sampling method be considered a cluster sample? Why or why not?
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