As its name implies, confidence intervals provide a range of valuesalong with a level of confidenceto 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 intervalvariability in the data, sample size, and confidence levelimpact the width of the interval.

For this question, 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:

Review Chapters 6 and 7 of the Frankfort-Nachmias & Leon-Guerrero text. In Chapter 7 (page 188), consider Hispanic migration and earnings, and focus on how different levels of confidence and sample size work together.

Review Magnusson's blog, found in the Learning Resources, to further your visualization and understanding of confidence intervals.

Use the Course Guide and Assignment Help, found in the Learning Resources, to search for a quantitative article related to confidence intervals.

Using the SPSS software, open the General Social Survey dataset, and choose a quantitative variable that interests you.

Using SPSS:

Take a random sample of 100.

Calculate the 95% confidence interval for the variable.

Calculate a 90% confidence interval.

Take another random sample of 400.

Calculate the 95% confidence interval for the variable.

Calculate a 90% confidence interval.

Respond to this question with your results 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 usingor not usingconfidence intervals. Provide examples based on the results of your data. Also, use your research to support your findings.

support the response with reference to scholarly evidence