Question

Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page listings. b) We want to know what percentage of local businesses anticipate hiring additional employees in the upcoming month. We randomly select a page in the Yellow Pages and call every business listed there.

Short answer

The sampling methods in both situations are not appropriate due to potential bias and lack of representation.

Step-by-step solution

Understand the Problem

First, identify the key elements of each situation. In part (a), we need to determine whether the method of randomly calling 50 doctors from Yellow Page listings will provide a representative sample for finding out what percentage accept Medicaid patients. In part (b), we need to assess if selecting one page and calling every business on it can accurately represent the hiring plans of all local businesses.

Analyze Sampling Method - Situation (a)

In situation (a), calling 50 randomly selected doctors from the Yellow Pages may not give an accurate representation since the list might not be comprehensive or updated. Additionally, using Yellow Pages could introduce bias if it doesn't list all doctors equally, such as those newer to the community or those not advertising there.

Analyze Sampling Method - Situation (b)

For situation (b), choosing one page from the Yellow Pages and calling every business on that page is likely to introduce significant bias. This approach doesn't ensure that all types of businesses are included, as the page may contain a cluster of similar types of businesses that do not represent the entire local business population.

Conclusion

Overall, both sampling methods are flawed. In situation (a), the random selection lacks breadth and might not be reflective of all doctors. In situation (b), the selection based on a single page introduces bias due to potential homogeneity of listed businesses.

Key concepts

Representative Sample

A representative sample is a critical concept in research and statistics, ensuring that the sample accurately reflects the population from which it is drawn. When a sample is representative, findings can be generalized to the larger population. This means that every relevant subgroup within the population should be proportionally included. Using the Yellow Pages to sample doctors, as in part (a) of the original exercise, may not produce a representative sample. This is because the directory might not list all practitioners, especially newer or less-publicized ones.

To enhance representativeness, the sample should be drawn from a comprehensive and updated list that includes all members of the population. For instance, using a professional medical registry or database would likely yield a more representative group of doctors. When evaluating sampling methods, always consider whether all segments of the population have been adequately represented.

Survey Bias

Survey bias occurs when the results of a survey are systematically skewed due to how the sampling or data collection is conducted. In situation (b) from the original exercise, selecting only one page from the Yellow Pages to call businesses can lead to survey bias. This sampling method might capture a narrow group, like mostly retail stores, if those happen to be clustered on that page.

Common types of survey bias include coverage bias, where some members of the population are inadequately represented because they are not included in the sample source. This can inadvertently skew results, as seen with the potential homogeneity of businesses on a single page. To minimize bias:

• Use a diverse and complete list for sampling.
• Ensure randomization covers all business types.
• Verify that the sampling methodology includes all relevant sectors fairly.

Appropriate methods will help produce more reliable and valid results, allowing for accurate interpretations and decisions made from the survey data.

Random Sampling

Random sampling is a technique in which each member of a population has an equal probability of being selected. This method is often advocated to reduce bias and enhance the representativeness of samples. Random sampling was attempted in both situations of the original exercise but was flawed.

In part (a), randomly selecting 50 doctors from the Yellow Pages assumes that this list is unbiased and complete, which isn't guaranteed. In part (b), even though a random page was selected, there was no randomness in the selection of businesses because all businesses on a single page were chosen.

To properly implement random sampling, the sample should be drawn from an exhaustive list where each entry has an equal chance of selection. Consider using computerized random number generators to select participants, ensuring that every individual or business in the database has an equal opportunity to be picked. Proper random sampling helps ensure that the sample is both unbiased and truly representative of the entire population.