Define And Provide An Example For Each Design Method

Define and provide an example for each design method

Assignment Answer the following problems showing your work and explaining (or analyzing) your results. 1. Define the following terms in your own words: population, sample, bias, design, response bias. 2. Define and provide an example for each design method: simple random sampling, systematic sampling, stratified sampling, cluster sampling. 3. Choose one design method from the list above. Using your example, make a list of 2-3 advantages and 2-3 disadvantages for using the method. 4. The name of each student in a class is written on a separate card. The cards are placed in a bag. Three names are picked from the bag. Identify which type of sampling is used and why. 5. A phone company obtains an alphabetical list of names of homeowners in a city. They select every 25th person from the list until a sample of 100 is obtained. They then call these 100 people to advertise their services. Does this sampling plan result in a random sample? What about a simple random sample? Explain why or why not. 6. The manager of a company wants to investigate job satisfaction among its employees. One morning after a meeting, she talks to all 25 employees who attended. Does this sampling plan result in a random sample? What type of sample is it? Explain. 7. An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects 10 schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? What type of sample is it? Explain. 8. Fifty-one sophomore, 42 junior, and 55 senior students are selected from classes with 516, 428, and 551 students respectively. Identify which type of sampling is used and explain your reasoning. 9. You want to investigate the workplace attitudes concerning new policies that were put into effect. You have funding and support to contact at most 100 people. Choose a design method and discuss the following: i. Describe the sample design method you will use and why. ii. Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.? iii. Discuss the bias, on the part of both the researcher and participants. 10. A local newspaper wanted to gather information about house sales in the area. It distributed 25,000 electronic surveys to its readers asking questions about house sales in the past 6 months. Of the surveys sent out, 3.2% were returned. The results found that 92% of people did not sell their house in the past 6 months and 85% of people would expect a loss if they sold their house. The writer wants to use these results to conclude that the housing market is declining, and we are headed for a recession. Explain the bias and sampling error in this study. Should the writer conclude that the housing market is declining based upon this data? Why or why not? 11. Using the same data example collected in the first assignment, you will continue to collect data for another 5–10 days. Write a paper (1–3 pages) including all of the following content: a. Recalculate the mean, standard deviation, and variance. b. Is your mean increasing or decreasing? c. Explain the effects of the larger sample size in relation to your data. d. Do you think the current sample you have is enough to draw an accurate conclusion, or do you need a larger sample? e. What conclusions can you draw from comparing both sets of data?

Paper For Above instruction

The assignment encompasses several aspects of sampling methods, biases, and interpretation of data analysis, aimed at understanding key statistical concepts and their applications in real-world scenarios. The initial task is defining foundational terms like population, sample, bias, design, and response bias in one’s own words. These definitions set the groundwork for further exploration of sampling techniques, including simple random sampling, systematic sampling, stratified sampling, and cluster sampling, each explained with an illustrative example.

Definitions of Key Terms

Population refers to the entire group of individuals or items that are the focus of a study, such as all residents in a city or all students in a school. A sample is a subset of the population selected for analysis, representing the larger group. Bias describes any systematic error that distorts the results, leading to incorrect conclusions. Response bias occurs when respondents give inaccurate answers due to factors like social desirability or misunderstanding. The design of a study encompasses the plan and method used to collect, analyze, and interpret data, ensuring the results are valid and reliable.

Sampling Methods with Examples

Simple random sampling involves selecting individuals from a population entirely by chance, giving each member an equal probability of inclusion. For example, randomly choosing 50 students from a school to survey about their study habits. Systematic sampling selects every kth individual from an ordered list; for example, selecting every 10th person from a registration list. Stratified sampling divides the population into subgroups based on shared characteristics, then randomly samples from each group—such as sampling equal numbers of males and females from a population. Cluster sampling involves dividing the population into clusters (like city blocks), randomly selecting entire clusters, and including all members within those clusters, such as surveying all households in selected neighborhoods.

Advantages and Disadvantages of Stratified Sampling

Choosing stratified sampling for detailed analysis, its advantages include increased precision by ensuring representation across subgroups, and efficiency in smaller samples. However, it can be costly and time-consuming to identify and categorize subgroups, and complex to implement when the population structure is not well known.

Identification of Sampling Types in Examples

In the case where three students' names are randomly picked from a bag, the sampling method is simple random sampling, because each student has an equal chance of being selected. The city’s systematic sampling plan, selecting every 25th name, is a systematic sampling method. This method is not purely random because the starting point could bias the sample if there's an underlying pattern in the list. The company’s systematic selection does not result in a simple random sample, as it does not give all individuals an equal chance, but it can produce a representative sample if the list is random.

Analysis of Specific Sampling Plans

The sampling plan where a manager interviews all employees who attended a meeting results in a convenience sample, which is not random because the sample is based on availability rather than randomness. Similarly, selecting all teachers from randomly chosen schools amounts to cluster sampling. While it captures data across several schools, it does not meet the criteria of a simple random sample since not every teacher had an equal chance of selection. The stratified sample based on class year shows proportional sampling matching the overall student distribution, thus representing the composition of the population accurately.

Design Method for Workplace Attitudes Study

Given funding constraints, a stratified random sampling method would be appropriate. The population includes all employees, with particular attention to departments or roles—such as full-time staff in managerial, technical, and administrative positions. This approach minimizes bias by ensuring various groups are represented. Potential biases include non-response or participant self-selection, which might skew results if certain groups are less likely to respond, and researcher bias in choosing specific departments or individuals.

Bias and Sampling Error in Housing Market Survey

The low response rate (3.2%) introduces non-response bias, as those who respond may differ significantly from non-respondents, leading to inaccurate estimates. The sampling error arises because the sample is not representative of the entire population. The survey's bias, primarily due to self-selection, means the results indicating that most respondents did not sell houses or expect losses may not reflect the entire housing market. Thus, the conclusion that the market is declining lacks robust support without addressing these biases.

Ongoing Data Collection and Analysis

Continuing to collect data over additional days allows recalculation of statistical measures—mean, standard deviation, and variance—to observe trends and stability in the data. An increase or decrease in the mean could suggest emerging trends in attitudes or behaviors. Larger sample sizes tend to decrease sampling error, resulting in more precise estimates. However, ensuring the sample remains unbiased is equally important. Comparing this expanded dataset with the original helps determine whether initial conclusions hold or need revision, thus supporting more accurate decision-making.

Conclusion

Understanding sampling techniques, biases, and statistical analysis is crucial in research to draw valid conclusions. Employing appropriate sampling methods reduces bias and enhances the reliability of findings. Recognizing biases such as non-response and sampling error informs better interpretation of data trends. Continuous data collection and analysis refine these insights, promoting informed decision-making in various fields, from market analysis to social sciences. Proper application of these principles ensures the integrity and usefulness of research outcomes.

References

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