"Identify the population and the sample. Describe the sample data set.
To gather information about starting salaries at companies listed in the Standard & Poor’s 500, a researcher contacts 74 of the 500 companies."

Verified step by step guidance

1. Step 1: Understand the concept of population and sample. The population refers to the entire group being studied, while the sample is a subset of the population selected for analysis.
2. Step 2: Identify the population in this problem. The population consists of all companies listed in the Standard & Poor’s 500 index, which totals 500 companies.
3. Step 3: Identify the sample in this problem. The sample is the 74 companies that the researcher contacted out of the 500 companies in the population.
4. Step 4: Describe the sample data set. The sample data set includes information about the starting salaries at the 74 companies contacted by the researcher. This data is a subset of the larger population data.
5. Step 5: Recognize the importance of sampling. Sampling allows researchers to gather insights about the population without needing to contact every single company, which can save time and resources.

Key Concepts

Population

In statistics, the population refers to the entire group of individuals or items that share a common characteristic, from which a sample can be drawn. In this context, the population consists of all 500 companies listed in the Standard & Poor’s 500 index. Understanding the population is crucial for making inferences about the broader group based on the sample data.

Sample

A sample is a subset of the population selected for analysis, intended to represent the larger group. In this scenario, the sample comprises the 74 companies contacted by the researcher. Analyzing the sample allows researchers to estimate characteristics, such as starting salaries, of the entire population without needing to survey every member.

Sample Data Set

The sample data set refers to the collection of data obtained from the selected sample. In this case, it would include the starting salaries reported by the 74 contacted companies. This data set is essential for statistical analysis, as it provides the basis for drawing conclusions and making predictions about the population's starting salaries.