Question

Describe the sample and describe a reasonable population. A cell phone carrier sends a satisfaction survey to 100 randomly selected customers.

Short answer

In this context, the 'sample' is the 100 randomly selected customers who received the satisfaction survey from the cell phone carrier. A reasonable 'population' for this exercise would be all customers of the cell phone carrier.

Step-by-step solution

Identify the Sample

The exercise directly mentions the 'sample' being considered. Here, it is the 100 randomly selected customers who received the satisfaction survey from the cell phone carrier.

Propose a plausible Population

Based on the sample information provided, a possible population would comprise all customers of the cell phone carrier. These are the individuals about whom the cell phone carrier wants to understand satisfaction levels. Therefore, they form the larger group of interest (population) from which the sample was drawn.

Key concepts

Sampling Methods

When conducting research in statistics, sampling methods are crucial for selecting a subset of individuals from a population to estimate characteristics of the whole group. There are different types of sampling methods, which can vastly affect the validity and reliability of the research findings.

Key sampling methods include:

• Simple Random Sampling: Every member of the population has an equal chance of being selected. This method is exemplified in the exercise where 100 customers were randomly chosen by the cell phone carrier.
• Stratified Sampling: The population is divided into subgroups or strata, and random samples are then taken from each stratum. For instance, a cell phone carrier might divide customers by service plan before sampling.
• Cluster Sampling: The population is divided into clusters, usually geographically, and a random sample of clusters is chosen. All individuals within selected clusters are included in the sample.
• Systematic Sampling: Every nth member of the population is chosen. For example, every 10th customer in a billing list could be selected.
• Convenience Sampling: Individuals who are easily accessible are chosen. This method is often used in pilot studies but can be less reliable due to potential biases.

Choosing the right sampling method is vital for ensuring that the sample represents the population well and that the subsequent statistical analysis provides meaningful insights.

Survey Sampling

Survey sampling involves selecting a part of the population to question in order to draw conclusions about the whole. It's a critical tool for businesses, researchers, and policy makers to gather information on opinions, behaviors, or demographic characteristics.

The process of survey sampling typically follows these steps:

• Defining the target population.
• Choosing the most appropriate sampling method.
• Determining the sample size that is statistically significant.
• Executing the sampling process to gather the sample.
• Collecting responses from the selected individuals.
• Analyzing the results to make conclusions about the entire population.

The survey's quality significantly depends on how well the sample represents the population. As seen in the provided exercise, the cell phone carrier has randomly selected 100 customers, which, if done correctly, should help in minimizing selection biases and give a snapshot of the overall customer satisfaction. The insights derived from the survey could inform business strategies, marketing approaches, and customer service enhancements.

Customer Satisfaction Statistics

Customer satisfaction statistics measure how products and services meet or surpass customer expectations. These statistics are pivotal for businesses to evaluate their performance, identify areas for improvement, and maintain competitive advantage.

Key aspects of customer satisfaction statistics include:

• Customer Satisfaction Score (CSAT): A basic measure where customers rate their satisfaction with a service or product.
• Net Promoter Score (NPS): Measures the likelihood of customers to recommend a company's product or service to others.
• Customer Effort Score (CES): Assesses how much effort a customer has to exert to get an issue resolved, a service fulfilled, or a product purchased.

In the context of the exercise, the cell phone carrier would analyze the survey data to calculate these statistics, revealing insights into the quality of service provided to customers. The findings can help the carrier to tailor its offerings, address service issues, and ultimately improve customer loyalty and retention.