To prepare for this Discussion:• Review Chapters 6 and 7 of the Frankfort-Nachmias & Leon-Guerrero text and in Chapter 7, p. 188, consider Hispanic migration and earnings and focus on how different levels of confidence and sample size work together.• Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of confidence intervals.• Use the Course Guide and Assignment Help found in this week’s Learning Resources to search for a quantitative article related to confidence intervals.• Using the SPSS software, General Social Survey dataset and choose a quantitative variable that interests you.

Week 4: Discussion

Probability, Sampling Distributions, and Confidence Intervals

Learning Resources

Required Readings

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

· Chapter 5, “The Normal Distribution” (pp. 151-177)

· Chapter 6, “Sampling and Sampling Distributions” (pp. 179-209)

· Chapter 7, “Estimation” (pp. 211-240)

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.

· Chapter 3, “Selecting and Sampling Cases”

· Chapter 5, “Charts and Graphs”

· Chapter 11, “Editing Output”

Magnusson, K. (n.d.). Welcome to Kristoffer Magnusson’s blog about R, Statistics, Psychology, Open Science, Data Visualization [blog]. Retrieved from http://rpsychologist.com/index.html

As you review this web blog, select the Interpreting Confidence Intervals – new d3.js visualization link, once you select the link, follow the instructions to view the interactive for confidence intervals. This interactive will help you to visualize and understand confidence intervals.

Note: This is Kristoffer Magnusson’s personal blog and his views may not necessarily reflect the views of Walden University faculty.

Walden University Library. (n.d.). Course Guide and Assignment Help for RSCH 8210. Retrieved from http://academicguides.waldenu.edu/rsch8210

For help with this week’s research, see this Course Guide and related weekly assignment resources.

Datasets

Your instructor will post the datasets for the course in the Doc Sharing section and in an Announcement. Your instructor may also recommend using a different dataset from the ones provided here.

Optional Resources

Rice University, University of Houston Clear Lake, and Tufts University. (n.d.). Online Statistics Education: An Interactive Multimedia Course of Study. Retrieved from http://onlinestatbook.com/2/estimation/ci_sim.html

Use this website for your practice as you consider confidence intervals and how the width changes. Also, consider why the width might be important.

Skill Builders:

· Confidence Intervals

· Sampling Distributions

To access these Skill Builders, navigate back to your Blackboard Course Home page, and locate “Skill Builders” in the left navigation pane. From there, click on the relevant Skill Builder link for this week.

You are encouraged to click through these and all Skill Builders to gain additional practice with these concepts. Doing so will bolster your knowledge of the concepts you’re learning this week and throughout the course.

Discussion: The Importance of Relationships

As its name implies, confidence intervals provide a range of values, along with a level of confidence, to serve as an estimate of some unknown population value. Since it is rare to have access to the entire population, you must frequently rely on the confidence interval of the sample to make some inference abo

Assignment Task 2

Respond to one of your colleague’s posts in 125 words response and explain how you might see the implications differently.

Colleague Response

Romel Jimera

Top of Form

For this week’s discussion on the relationship between data variability, sample size, and confidence level, I chose the “Size of the Place in 1000s” as my quantifiable variable, utilizing the General Social Survey dataset. The mean Age from that dataset is 49.01. To better appreciate the tradeoff between lowering the risk of our confidence in estimations and increasing precision, I entered a random sample size of 100 and 400 with 90 and 95 percent confidence levels, using IBM SPSS Statistics software.

Table 1

In Table 1, the left table shows a random sample of 100, a mean of 324.90, and a standard error of 121.911. Using a 95% confidence interval (CI), the estimation was only 5% off (Frankfort-Nachmias et al., 2021). Meaning we are 95% confident that the actual average size of the place in 1000s is not less than 83 and not more than 566.8. However, with a 90% confidence level in the right table, all the values remain the same except for the CI (122.48, 527.32). Although the CI width is shorter than the previous one, there is more precision, but the chance of error has increased to 10%. Can we lower the error probability by expanding the sample size to 400?

Table 2

In Table 2, the left table displays a random sample of 400, which has a lower standard error of 48.931 than a smaller sample of 100. In a 95% CI, the width has become narrower, and the values of the lower and upper bounds (187.58, 379.96) are more proximate to the mean (283.77). By increasing the sample size, researchers can enhance the precision of their estimates by decreasing the CI width (Frankfort-Nachmias et al., 2021). Consequently, the sample size and the confidence interval width are inversely related. On the other hand, the right table shows the same outcome as the left table, but with a lower bound of 203.10 and an upper bound of 364.44, based on a 90% CI. Hence, the CI becomes more precise when decreasing the confidence level from 95% to 90%.

Confidence intervals are underutilized because they can lead to unjustified or arbitrary inferences (Morey et al., 2016), resulting in conclusions without sufficient evidence then requiring a larger sample size. However, they can be an efficient approach for statistical inference (Sim & Reid, 1999). For instance, on November 18, 2020, Pfizer summarized its Phase 3 study of the COVID-19 vaccine, resulting in a 95% probability of the vaccine efficacy rate between 90.3% and 97.6% (Wang, 2021). After the vaccine was made accessible to the public, the pooled efficacy of the vaccination in preventing mortality from COVID-19 was 96.1% (95% CI: 91.5–98.2%) (CDC, 2021). These studies provide a grounded illustration of the critical nature of CI.

While increasing the confidence level to minimize the error probability, the estimate becomes les

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