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You must choose an SRS of 10 of the 440 retail outlets in New York that sell your company's products. How would you label this population to select a simple random sample? (a) \(001,002,003, \ldots, 439,440\) (b) \(000,001,002, \ldots, 439,440\) (c) \(1,2, \ldots, 439,440\)

Short Answer

Expert verified
Label the population as 001 to 440 using option (a).

Step by step solution

01

Understand the Concept of Simple Random Sampling (SRS)

In simple random sampling (SRS), every individual member of the population has an equal chance of being selected. To achieve this, each individual must be distinguishable by a unique identifier.
02

Determine Labeling Requirements

When labeling a population for selection, it is crucial that all labels have the same number of digits. This ensures uniformity and prevents errors during the process of selection.
03

Analyze Labeling Options

Let's analyze the options: - Option (a): Labels range from 001 to 440. - Option (b): Labels range from 000 to 440. - Option (c): Labels range from 1 to 440. Options (a) and (b) maintain a consistent number of digits, which is necessary for selecting a truly random sample.
04

Identify the Correct Labeling Method

The best practice is to ensure all labels have the same number of digits starting from zero. Thus, the appropriate option is (a) where each label consistently uses a three-digit format like 001, 002, ..., 440.

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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 strategies used to select individual members from a population to participate in a study. There are several different types of sampling methods, each with its own strengths and weaknesses. However, the primary goal remains the same: to achieve a representative sample that accurately reflects the larger population.

For example, in the context of simple random sampling (SRS), each member of the population has an equal chance of being chosen. A fair comparison here is like drawing names out of a hat, where each name has an identical probability of being selected.
Other sampling methods include:
  • **Systematic Sampling**: Selecting every nth item from a list.
  • **Stratified Sampling**: Dividing the population into strata, or groups, and sampling from each group.
  • **Cluster Sampling**: Choosing clusters of participants from a larger population.
Each of these methods serves specific research needs and depends on the structure and characteristics of the target population.
Population Labeling
In sampling, particularly in simple random sampling, population labeling is crucial. It's the process of assigning an identifier to each member of the population, ensuring each has a unique and distinguishable label.

Labeling is important for:
  • **Ensuring accuracy** in selection and removing biases in simple random sampling.
  • **Facilitating randomization** by providing a numerical identifier to each member.
Effective population labeling requires consistency in the format. For instance, if you have 440 retail outlets, labels like 001 to 440 or 000 to 440 are optimal. Using a uniform digit format ensures clarity and reduces errors.
Furthermore, maintaining uniform labels aids in the execution of statistical processes by automating or simplifying the selection scenarios.
Statistical Sampling Techniques
Statistical sampling techniques are methods used to select samples that represent a larger population. They play a pivotal role in collecting data and making inferences about the entire population without surveying every individual.

Key aspects of statistical sampling techniques include:
  • **Randomness:** Ensures every member of the population has an equal chance of selection.
  • **Replicability:** Techniques should be documented and easy to reproduce in repeated studies.
  • **Minimum Bias:** Aim to reduce selection bias to maintain sample representation.
If employing simple random sampling, for example, the process often utilizes software or random number generators to pick labels, like choosing 10 out of 440 outlets accurately to reflect the whole.
Other techniques may account for subsets of populations, like using stratified sampling to capture demographic differences, which offers deeper insights per segment.

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Most popular questions from this chapter

An opinion poll calls 2000 randomly chosen residential telephone numbers in Portland and asks to speak with an adult member of the household. The interviewer asks, "How many movies have you watched in a movie theater in the past 12 months?" In all, 831 people respond. The sample in this study is (a) all adults living in Portland. (b) the 2000 residential phone numbers called. (c) the 831 people who responded.

A Survey of 100,000 Physicians. In 2010 , the Physicians Foundation conducted a survey of physicians' attitude about health care reform, calling the report "a survey of 100,000 physicians." The survey was sent to 100,000 randomly selected physicians practicing in the United States: 40,000 via postoffice mail and 60,000 via email. A total of 2,379 completed surveys were received. 11 (a) State carefully what population is sampled in this survey and what is the sample size. Could you draw conclusions from this study about all physicians practicing in the United States? (b) What is the rate of nonresponse for this survey? How might this affect the credibility of the survey results? (c) Why is it misleading to call the report "a survey of 100,000 physicians"?

Academic Dishonesty. A study of academic dishonesty among college students used a two-stage sampling design. The first stage chose a sample of 30 colleges and universities. Then, the study authors mailed questionnaires to a stratified sample of 200 seniors, 100 juniors, and 100 sophomores at each school. \({ }^{6}\) One of the schools chosen has 1127 freshmen, 989 sophomores, 943 juniors, and 895 seniors. You have alphabetical lists of the students in each class. Explain how you would assign labels for stratified sampling. Then use software, the Simple Random Sample applet, or Table B, starting at line 138 , to select the first four students in the sample from each stratum. After selecting four students for a stratum, continue to select the students for the next stratum.

Archaeologists plan to examine a sample of 2-meter-square plots near an ancient Greek city for artifacts visible in the ground. They choose separate samples of plots from floodplain, coast, foothills, and high hills. What kind of sample is this? (a) A simple random sample (b) A stratified random sample (c) A voluntary response sample

A sample of households in a community is selected at random from the telephone directory. In this community, \(4 \%\) of households have no telephone, \(10 \%\) have only cell phones, and another \(25 \%\) have unlisted telephone numbers. The sample will certainly suffer from (a) nonresponse. (b) undercoverage. (c) false responses.

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