Probability, Sampling Distributions, and Confidence Intervals

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

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

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


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

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 about the population of interest. Before making accurate inferences to the population, we need to fully understand how the three key components of the interval—variability in the data, sample size, and confidence level—impact the width of the interval.

For this Discussion, you will explore the relationship between these components and understand the trade-off between reducing risk in our confidence of estimates and increasing precision.

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.

Assignment Task Part 1:

Using SPSS:

1. Take a random sample of 100.

2. Calculate the 95% confidence interval for the variable.

3. Calculate a 90% confidence interval.

4. Take another random sample of 400.

5. Calculate the 95% confidence interval for the variable.

6. Calculate a 90% confidence interval.

Post your results, the mean of Age to verify the dataset you used, and an explanation of how different levels of confidence and sample size affect the width of the confidence interval. Next, consider the statement, “Confidence intervals are underutilized” and explain what the implications might be of using or not using confidence intervals. Provide examples based on the results of your data. Also, use your research to support your findings.

Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.

Assignment Task Part 2:

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

Be sure to citate appropriate references.

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