Lab 7 Template 1 Using The Data You Collected For Week 5

Lab 7 Template1 Using The Data You Collected For The Week 5 Lab Hei

Using the data you collected for the Week 5 Lab (heights of 10 different people that you work with plus the 10 heights provided by your instructor), discuss your method of collection for the values that you are using in your study (systematic, convenience, cluster, stratified, simple random). What are some faults with this type of data collection? What other types of data collection could you have used, and how might this have affected your study? Use the Week 6 Spreadsheet to help you with calculations for the following questions/statements.

Give a point estimate (mean) for the average height of all people at the place where you work. Start by putting the 20 heights you are working with into the blue Data column of the spreadsheet. What is your point estimate, and what does this mean?

Find a 95% confidence interval for the true mean height of all the people at your place of work. What is the interval?

Give a practical interpretation of the interval and explain carefully what the output means. (For example, you might say, "I am 95% confident that the true mean height of all of the people in my company is between 64 inches and 68 inches").

Post a screenshot of your work from the t value Confidence Interval for µ from the Confidence Interval tab on the Week 6 Excel spreadsheet.

Now, change your confidence level to 99% for the same data, and post a screenshot of this table/interval, as well.

Compare the margins of error from the two screenshots. Would the margin of error be larger or smaller for the 99% CI? Explain your reasoning.

Save this template with your answers and include your name in the title.

Submit the document.

Paper For Above instruction

The process of data collection is foundational in research studies, as it directly influences the validity, reliability, and interpretability of the findings. In the context of the Week 5 lab, where heights of individuals at a workplace were collected, the primary method employed was convenience sampling. This involved selecting ten individuals known personally or easily accessible, supplemented by ten heights provided by the instructor, creating a total sample of twenty heights. Convenience sampling is straightforward, cost-effective, and quick; however, it carries significant limitations, mainly the risk of selection bias which can impact the generalizability of the results. Such data may not be representative of the entire workforce if the sampled individuals differ systematically from those not included, in terms of height or other variables influencing height (Etikan, Musa, & Alkassim, 2016).

Other data collection methods like simple random sampling or stratified sampling could mitigate some of these biases. Simple random sampling involves selecting individuals entirely at random from the population, thereby ensuring each member has an equal chance of being included. This method enhances the representativeness of the sample and reduces selection bias but may require a comprehensive list of all members of the population (Creswell & Creswell, 2017). Stratified sampling involves dividing the population into strata based on characteristics (e.g., department, age, gender) and randomly sampling within each stratum, ensuring a more precise estimation when certain subgroups may differ significantly in height (Lohr, 2019). Implementing these alternative methods might have led to more accurate estimations of the average height, as they would better reflect the diversity of the entire population.

The point estimate, specifically the sample mean, provides an initial understanding of the average height at the workplace. Assuming the collected heights were entered into the blue Data column of the spreadsheet, the mean is calculated by summing all 20 heights and dividing by 20. For example, if the sum of these heights is 1,280 inches, the mean height would be 64 inches. This point estimate indicates the best single value derived from the sample to approximate the true population mean, although it is subject to sampling variability. It serves as a basis for constructing confidence intervals to gauge the precision of this estimate.

Constructing a 95% confidence interval involves using the sample mean along with the standard deviation and the appropriate t-value for the sample size. The standard error (SE) is calculated by dividing the sample standard deviation (s) by the square root of the sample size (n=20). Multiplying this SE by the t-value corresponding to 19 degrees of freedom (approximately 2.093) yields the margin of error (MoE). The confidence interval is then expressed as: mean ± MoE. For instance, if the mean is 64 inches and the MoE is 1.5 inches, the interval would be from 62.5 to 65.5 inches. This interval means that we are 95% confident that the true average height of all employees falls within this range, based on the sample data and assuming the sampling distribution is approximately normal (Row, 2014).

Interpreting the interval practically, one could state, “We are 95% confident that the true mean height of all employees at the workplace is between 62.5 inches and 65.5 inches.” This provides a range within which the population mean likely resides, acknowledging sampling uncertainty. It is important to understand that this does not mean there is a 95% probability that the true mean is within this specific interval; rather, in repeated sampling, 95% of such calculated intervals would contain the true mean (Creswell & Creswell, 2017).

In the context of changing the confidence level from 95% to 99%, the corresponding t-value increases (approximately 2.861 with the same degrees of freedom), which results in a larger margin of error. When the interval width expands, the confidence interval becomes wider, reflecting increased certainty; however, it also indicates less precision in the estimate (Lohr, 2019). The wider interval at 99% confidence assures a higher probability that the true mean is within the range but at the cost of decreased specificity. Comparing the margins of error confirms this: the margin at 99% will be larger than at 95%, indicating a trade-off between confidence level and estimate precision.

These differences underscore important considerations in statistical reporting and decision-making. A higher confidence level provides greater assurance that the interval contains the true mean but reduces the estimate’s precision. Researchers and practitioners must balance the need for confidence with the desire for detailed, narrow estimates depending on the context and application (Creswell & Creswell, 2017).

In conclusion, the choice of data collection method heavily influences the quality of research findings, with convenience sampling being less ideal compared to probabilistic methods like simple random or stratified sampling. Calculating and interpreting confidence intervals for the mean provides critical insights into the reliability and accuracy of estimates, with higher confidence levels resulting in more conservative, wider intervals. Proper understanding and application of these statistical tools are essential in making informed, evidence-based decisions in research and practice.

References

• Creswell, J. W., & Creswell, J. D. (2017). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (5th ed.). SAGE Publications.
• Etikan, I., Musa, S. A., & Alkassim, R. S. (2016). Comparison of Convenience Sampling and Probability Sampling. American Journal of Theoretical and Applied Statistics, 5(1), 1-4.
• Lohr, S. L. (2019). Sampling: Design and Analysis (2nd ed.). CRC Press.
• Row, R. (2014). Confidence Intervals. In Introduction to Statistics. OpenStax CNX. https://cnx.org/contents/... (Accessed 2023).
• Lang, T. A., & Secic, M. (2006). How to Report Statistics in Medicine. American College of Physicians.