Problem 8 - Basic Statistics for Business and Economics with Student

Question

For the following questions, would you collect information using a sample or a population? Why? a. Statistics 201 is a course taught at a university. Professor A. Verage has taught nearly 1,500 students in the course over the past 5 years. You would like to know the average grade for the course. b. As part of a research project, you need to report the average profitability of the number one corporation in the Fortune 500 for the past 10 years. c. You are looking forward to graduation and your first job as a salesperson for one of five large pharmaceutical corporations. Planning for your interviews, you will need to know about each company's mission, profitability, products, and markets. d. You are shopping for a new MP3 music player such as the Apple iPod. The manufacturers advertise the number of music tracks that can be stored in the memory. Usually, the advertisers assume relatively short, popular music to estimate the number of tracks that can be stored. You, however, like Broadway musical tunes and they are much longer. You would like to estimate how many Broadway tunes will fit on your MP3 player.

Step-by-Step Solution

Answer

a. Population; b. Population; c. Population; d. Sample.

Step 1: Define Sample and Population

A sample is a subset of individuals or items from a larger population used to make inferences about the population. A population includes all members or items of a particular group that meet certain criteria.

Step 2: Analyze Exercise a

You want to know the average grade of the course for all students taught by Professor A. Verage over the past 5 years. Since nearly 1,500 students constitute a manageable number, it's feasible to consider the entire group as a population. Therefore, collecting information would be based on a population, not a sample.

Step 3: Analyze Exercise b

The question involves reporting on the average profitability of a single corporation over the past 10 years. Since you are examining the financial performance of this one corporation for each of the years, you are working with a complete set of data points, making it a population instead of a sample.

Step 4: Analyze Exercise c

In this scenario, you need detailed information about five pharmaceutical corporations. Because the number of corporations is small (five) and defines the complete group of interest, you can treat this as a population, bypassing the need to sample.

Step 5: Analyze Exercise d

When estimating how many Broadway tunes can fit on an MP3 player, you are dealing with the variability in the length of Broadway tunes, which are the subjects of interest. As it is unattainable to measure every tune, you would collect data from a sample of Broadway tunes to make inferences about the population of all Broadway tunes.

Key Concepts

Sample and Population

Understanding the difference between a sample and a population is crucial in statistics. A population refers to the entire set of elements about which we want to gather information. This could include all students in a university, all corporations in a market, or even all Broadway tunes ever produced. On the other hand, a sample is a smaller group selected from this population, used to make statistical inferences about the entire group.

We opt to study a sample when the population is too large or too impractical to study in its entirety. In exercise a, since the group of students taught by Professor A. Verage total 1,500, you can actually use the whole group, making them the population. However, for exercise d, where it's about estimating how many Broadway tunes fit on a player, measuring every possible tune would be impractical, thus necessitating a sample for manageable data collection.

Data Analysis

Once you have identified your sample or population, the next step is data analysis. This process involves collecting, organizing, displaying, and examining the data to uncover patterns or insights. It is essential to choose the right method of analysis based on whether you are working with a sample or a population.

In exercise b, since you have data from one corporation over ten years, you can treat this as a population. Here, you would use complete data analysis since you're looking at all possible data points. In contrast, if it were a sample, you might utilize descriptive statistics to summarize the sample data and inferential statistics to make predictions or generalize findings. Good analysis helps in making informed decisions and drawing valid conclusions.

Inference Making

Inference making is a significant aspect of statistical analysis, particularly when dealing with samples. It allows us to generalize findings from a sample back to the larger population. When working with a sample, statisticians make use of inference to draw conclusions about the population from which the sample was taken.

In exercise d, by sampling a set of Broadway tunes, you make inferences about the entire population of Broadway tunes regarding storage on an MP3 player. Conversely, in exercises like a or b, where you're working with a whole population, you are reporting on complete data rather than making inferences. The accuracy of the inferences largely depends on the sample size and how representative it is of the population. This is why selecting an appropriate sample is a critical step in the research process.