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Chapter 1: Problem 42

Indicate whether each of the following constitutes data collected from a population or a sample. a. A group of 25 patients selected to test a new drug b. Total items produced on a machine for each year from 2001 to 2015 c. Yearly expenditures on clothes for 50 persons d. Number of houses sold by each of the 10 employees of a real estate agency during 2015

Short Answer

Expert verified
Statement a and c are data collected from a sample, while statement b and d pertains to a population.

Step by step solution

01

Understanding Data Type for Statement a

Analyzing statement a: 'A group of 25 patients selected to test a new drug', we can see that it refers to a selected group within a larger population. Therefore, this is data collected from a sample.
02

Understanding Data Type for Statement b

Looking at statement b: 'Total items produced on a machine for each year from 2001 to 2015', this is data collected on all items produced by the machine during this time period. Hence, it is data collected from a population.
03

Understanding Data Type for Statement c

In statement c: 'Yearly expenditures on clothes for 50 persons', unless the entire population we are studying consists of these 50 people, this is data collected from a sample.
04

Understanding Data Type for Statement d

Examining statement d: 'Number of houses sold by each of the 10 employees of a real estate agency during 2015', this represents data from all 10 employees, which suggests it is data collected from a population, assuming that only these 10 employees are part of the study.

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Key Concepts

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

Population vs Sample
In the realm of statistics, understanding the difference between a population and a sample is crucial for analyzing data correctly. Let's delve into what these terms mean and how they are applied in real-world data collection scenarios.
  • A population includes every possible element or outcome within a given dataset. It is the complete set of items that we are interested in studying. For example, if we want to know the average height of all the students in a university, our population would be all the students at that university.
  • A sample, on the other hand, is a subset of the population that is selected for analysis. When it is impractical or impossible to collect data from the entire population due to its large size, a sample is chosen to represent the population. For instance, evaluating the effectiveness of a new drug on only 25 patients selected randomly from a larger group of patients involves working with a sample.
Knowing whether data represents a population or a sample is important, as it dictates the type of statistical methods used and affects the reliability and validity of conclusions drawn from the data.
Statistical Analysis
Statistical analysis involves directly examining data to understand patterns, relationships, and trends. It is a vital aspect of many fields, including medicine, business, and social sciences, allowing professionals to make informed decisions based on data.
Here are key points about statistical analysis:
  • Descriptive Statistics help summarize and describe features of a dataset. This can include measures such as mean, median, mode, range, and standard deviation, which provide insights into the data's central tendency and variability.
  • Inferential Statistics enable researchers to draw conclusions and make predictions about a population, based on a sample. Statistical methods like hypothesis testing and confidence intervals allow for estimations of population parameters.
By applying statistical analysis, one can determine the validity of changes or differences in data, corroborate hypotheses, and provide insights that are crucial for decision-making processes.
Data Types in Statistics
In statistics, understanding different data types is essential for selecting appropriate methods of analysis and interpretation. Data in statistics can typically be categorized as follows:
  • Quantitative Data: This type of data is numerical and can be measured. It can be further classified into:
    • Discrete Data: Countable numbers, such as the number of houses sold by employees.
    • Continuous Data: Measurable quantities that can take any value within a range, such as yearly expenditures.
  • Qualitative Data: Non-numerical data that describes categories or qualities. It includes:
    • Nominal Data: Categories without a natural order, like types of clothing items.
    • Ordinal Data: Categories with a natural order, but differences between them are not precisely measurable.
Selecting the correct approach to data collection and analysis hinges on the proper identification and classification of these data types, impacting the accuracy of conclusions drawn from statistical studies.

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Most popular questions from this chapter

Explain the meaning of the following terms. a. Quantitative variable b. Qualitative variable c. Discrete variable d. Continuous variable \(e_{\text {Quantitative data }}\) f. Qualitative data

Explain the following. a. Random sample b. Nonrandom sample c. Convenience sample d. Judgment sample e. Quota sample

Classify the following quantitative variables as discrete or continuous. a. The amount of time a student spent studying for an exam b. The amount of rain last year in 30 cities c. The amount of gasoline put into a car at a gas station d. The number of customers in the line waiting for service at a bank at a given time

A survey of families living in a certain city was conducted to collect information on the following variables: age of the oldest person in the family, number of family members, number of males in the family, number of females in the family, whether or not they own a house, income of the family, whether or not the family took vacations during the past one year, whether or not they are happy with their financial situation, and the amount of their monthly mortgage or rent. a. Which of these variables are qualitative variables? b. Which of these variables are quantitative variables? c. Which of the quantitative variables of part \(\mathrm{b}\) are discrete variables? d. Which of the quantitative variables of part \(\mathrm{b}\) are continuous variables?

Explain the following four sampling techniques. a. Simple random sampling b. Systematic random sampling c. Stratified random sampling d. Cluster sampling
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