?Linda Kalof, Professor, Author? Our daily lives revolve around things that we cannot control. Before we step out the front door we ask, will it rain today?

Week 4: Probability, Sampling Distributions, and Confidence Intervals

Life is filled with uncertainty.

—Thomas Dietz, Professor, Author

—Linda Kalof, Professor, Author

Our daily lives revolve around things that we cannot control. Before we step out the front door we ask, will it rain today? What is the chance of getting stuck in traffic? Or better yet, will my class be cancelled? Even though Dietz and Kalof (2009) suggest that life is uncontrollable, we still try to feel a small sense of control through a smart use of statistics. Probability helps us to understand and cope with the seemingly uncertain decisions of life.

Uncertainty is also present in our samples since we rarely have the ability to measure the entire population. Understanding probability also assists us in obtaining accurate, representative samples. From probability-based samples we can construct confidence intervals to obtain a range of values in which our population value may lie.

In this week, you will explore probability as it relates to an observed occurrence. You also will explore the concept of the sampling distribution as well as confidence intervals of specific data. Finally, you explore the results of data to determine implications for social change.

Learning Objectives

Students will:

· Evaluate various distributions

· Evaluate confidence intervals

· Create visual displays of data

· Analyze data from datasets

· Analyze implications for social change

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.

By Day 3

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.

By Day 5

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

REFERENCES

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”

·

http://rpsychologist.com/index.html

http://academicguides.waldenu.edu/rsch8210

http://onlinestatbook.com/2/estimation/ci_sim.html

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.

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