# explore the relationship between these components and understand the trade-off between reducing risk in our confidence of estimates and increasing precision.

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 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.