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Chapter 11: Problem 5

Determine whether the sampling is dependent or independent. A sociologist wishes to compare the annual salaries of married couples. She obtains a random sample of 50 married couples in which both spouses work and determines each spouse's annual salary.

Short Answer

Expert verified
The sampling is dependent.

Step by step solution

01

Understand the Problem

The goal is to determine if the samples taken are dependent or independent. In this case, we need to compare the annual salaries of married couples.
02

Define Dependent and Independent Samples

Dependent samples are related to each other and often involve paired data, like measurements from the same subject before and after a treatment. Independent samples are not related and are drawn separately from different populations.
03

Analyze the Given Situation

The sociologist is comparing the annual salaries of married couples, specifically where both spouses in each couple work, and comparing their salaries as pairs.
04

Check the Relationship Between Samples

Since each spouse's salary is paired with their partner鈥檚 salary within the same couple, the samples are inherently related.
05

Conclusion

Based on the relationship that each spouse's salary is connected to their partner鈥檚 salary, the sampling of the annual salaries of married couples is dependent.

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Key Concepts

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

Sampling Methods
When conducting a statistical study, choosing the right sampling method is crucial. Sampling methods refer to the techniques used to select individuals or units to be observed in a study. These methods can be broadly classified into two categories:
  • Random Sampling: In this method, every individual in the population has an equal chance of being selected. This ensures that the sample is representative of the entire population.
  • Non-Random Sampling: This method does not provide every individual with an equal chance of selection. It might be easier or cheaper, but it can lead to biased results.
In our exercise, the sociologist uses random sampling to select 50 married couples. This ensures that the sample is representative of the population of married couples where both spouses work. Random sampling helps to eliminate biases that might affect the outcome of the study.
Paired Data
Paired data refers to data sets in which each data point in one set is related to a unique data point in another set. This is often the case in studies where measurements are taken from the same subjects under different conditions or from related subjects.
  • Examples of Paired Data: Heights of twins, before-and-after measurements in a treatment study, and, as in our exercise, salaries of married couples.
In our example, the data are naturally paired because each spouse's salary is connected to their partner鈥檚 salary. This pairing is essential because it allows for a more accurate comparison of salaries by accounting for the inherent relationship between the two data points in each pair. Paired data is crucial when determining if samples are dependent (related) or independent (unrelated).
Statistical Analysis
Statistical analysis is the process of collecting, analyzing, interpreting, and presenting data. It's used to discover patterns and trends, make predictions, and support decision making. Analyzing dependent samples, as in the case of our exercise, often requires different techniques compared to independent samples.
  • Tests for Dependent Samples: When analyzing dependent samples, paired sample t-tests are often used to compare the means of two related groups.
  • Tests for Independent Samples: For independent samples, independent two-sample t-tests are used to compare the means of two different groups.
In the sociologist鈥檚 study, the appropriate statistical analysis would involve techniques that account for the pairing of salaries, ensuring the comparison accurately reflects the relationship between each pair. This type of analysis provides more reliable results by considering the natural pairing in the data.

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