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Telephone Service Suppose a telephone company executive wishes to select a random sample of \(n=20\) (a small number is used to simplify the exercise) out of 7000 customers for a survey of customer attitudes concerning service. If the customers are numbered for identification purposes, indicate the customers whom you will include in your sample. Use the random number table and explain how you selected your sample.

Short Answer

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Short Answer Question: Explain the process of selecting a random sample of 20 customers from 7000 using a random number table.

Step by step solution

01

Understand Selection Criteria

To select the 20 random sample customers from 7000, we need to assign numbers to the customers. Since we have a total of 7000 customers, we will have a range of numbers from 0001 to 7000. Now we'll use the random number table to select 20 random samples from the given range.
02

Obtain a Random Number Table

A random number table is a series of digits (0-9) that are generated randomly and arranged in a table format. Each digit in the table will be unrelated to the previous or the next digit. The table ensures that each digit has an equal opportunity to be drawn during sampling. In the next step, we will consult this table to select customers.
03

Select Random Samples

To begin, we choose a starting point in the random number table, such as the top left corner. As we move through the table, we select groups of 4-digit numbers since we need to choose a sample from a range of 0001 to 7000. If a number is outside this range, we move on to the next 4-digit number until we gather 20 valid samples.
04

Explain the Selection Process

The selection process using a random number table ensures unbiased sampling by giving an equal chance to every customer within the range. By using this method, the telephone company executive can be confident about the randomization of the chosen sample, which helps provide accurate insights into customer attitudes towards the service.
05

Present Selected Sample

After going through the random number table and picking out 20 valid numbers within the specified range, we would list them out as a part of the selected sample for the survey. For example: 1234, 2587, 3719, 4820, 5923, 6072, 6281, 7000, 1792, 3250, 4798, 5289, 6888, 2447, 3195, 4138, 4766, 5641, 2026, 3553 Note that these numbers may not be the actual values you would get from a random number table. However, by following the steps above, you will get the required random sample of 20 customers from a population of 7000 customers for the survey.

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Key Concepts

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

Random Number Table
A random number table is an essential tool in statistics for selecting random samples. It is a chart filled with digits ranging from 0 to 9 arranged in no particular order. The beauty of these tables is their unpredictability.
The numbers are generated through random processes that ensure each digit has the same chance of appearing. This characteristic makes random number tables a reliable method for ensuring the randomness of sample selection.
When using a random number table, you start by choosing a point and then read a sequence, often skipping numbers that don't fit your criteria. This is crucial when needing a specific range, as seen in the selection of numbers from 0001 to 7000.
  • Random number tables remove human bias in number selection.
  • They are ideal in scenarios needing fairness and randomness.
  • Each number's appearance is independent of its neighbors.
Their use is widespread in studies requiring random sampling, like surveys and experiments.
Unbiased Sampling
Unbiased sampling is the cornerstone of reliable data collection and analysis. It refers to a sampling method where every member of the population has an equal chance of being selected.
In the telephone company's scenario, using a random number table ensures that the selection process is free from human bias. This method helps in getting a truly representative sample, reflecting the entire population's characteristics.
Benefits of unbiased sampling include:
  • Improved accuracy in data representations.
  • Removal of subjective influence in selecting sample members.
  • Better generalization of survey results to the entire population.
By maintaining an unbiased approach, the organization can have more confidence in the survey results, as they are more likely to accurately capture the customers' sentiments.
Customer Survey
Conducting a customer survey is an effective strategy for gathering insights and opinions from customers. This process involves selecting a group of individuals from a larger population to gain an understanding of their attitudes, beliefs, or experiences.
For the telephone company, the survey aims to gauge customer satisfaction and expectations regarding their services. Selecting a good sample is critical in ensuring the survey results are valid and useful.
Key roles of customer surveys:
  • Identifying customer needs and pain points.
  • Improving product and service offerings based on feedback.
  • Building a strong connection between the company and its clientele.
A well-conducted survey can lead to enhanced customer loyalty and can guide strategic decisions based on real customer data.
Sampling Process
The sampling process is a systematic way of selecting a portion of a population for study. It is crucial when dealing with large populations where it is impractical to examine every member.
In this exercise, the sampling process begins with defining the population, which consists of 7000 customers. The next step involves determining the sample size, which is 20 in this instance, ensuring it is manageable yet representative.
How the sampling process works:
  • Define the population and sample size.
  • Select a sampling method like random sampling.
  • Execute the sampling using tools, such as random number tables.
By carefully executing each step, the process ensures the sample represents the broader population, leading to more valid and credible results. The telephone company's ability to make informed decisions based on a well-executed sampling process underscores its importance.

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