Confidence intervals can be used to estimate population parameters such as means or proportions. Their accuracy is defined with the confidence level. The most common confidence levels are 90%, 95%, and 99%. It is a trade-off between achieving greater confidence in making an estimate and the precision of that estimate. Although using a 99% level increased our confidence level from 95% to 99% (thereby reducing our risk of being wrong from 5% to 1%), the estimate became less precise as the width of the interval increased. A larger sample size will result in a smaller confidence interval with a smaller margin of error. A smaller sample size will result in a wider confidence interval with a larger margin of error ( Frankfort-Nachmias et al,2021).
CIs are not intuitive because it dose not depend on luck itâ€™s a probability estimation of a random interval. Confidence intervals let us quantify our uncertainty about an estimate in the form of a range of values.
Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2021). Social statistics for a diverse society. SAGE Publications, Inc.
The mean age of the respondents was 49.59 years. The random sample of the population for Rs occupational prestige score (2010) was 100 from a total of 607 respondents. The smaller the sample and the lower confidence level (CI) used can indicate a higher margin of error (Frankfurt-Nachmias et al., 2021). Increasing the CI can predict how a population mean from a random sample can potentially fall within an interval range (Frankfurt-Nachmias et al., 2021). The sample size and the higher the CI, both play a key role in reducing the margin of error. For example, using a larger sample or increasing the CI percentage will reduce errors and the width of the confidence interval will be shorter (Frankfurt-Nachmias et al., 2021, Walden University, 2021).
Descriptive Distribution Explanation
A random sample of 100 respondents was taken using the confidence intervals of 90 and 95%. The mean was 44.35 with a standard error of 1.401 for both confidence intervals. The population mean (90% CI) will fall between 42.03-46.68. The population mean (95% CI) will fall between 41.57-47.14.
We took a random sample of 400 of the 607 respondents again using both CI. The mean was 45.21 with a standard error of 0.684. The population mean (90% CI) will fall between 44.08-46.34. Population mean (95% CI) will fall in the range of 43.86-46.55. The larger sample shows a reduction in the margin of error increasing the possibility for the population mean to fall within the CI rather than increasing the CI.
It is better if researchers use CI to show a range of data rather than a single data point to explain how data from a random sample can be applied to a larger group or population (Frankfurt-Nachmias et al., 2021). CI and sample sizes influence one another and how accurate the selected data apply to a certain population as evidenced in example Hispanic Migration and Earnings (Frankfurt-Nachmias et al., 2021). Researchers utilized odds ratios and CI to show how respondents in drug abuse study were likely to report drug use and utilizing treatment was higher in non-Hispanic and Hispanic males than African American males with income $5000 than those who earn less or receive public assistance. (Small, 2016).
Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2021). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publication.
Small, L. F. F. (2016). Co-Morbidities Among Persons with Substance Abuse Problems: Factors Influencing the Receipt of Treatment. Journal of Drug Issues, 46(2), 88-101. http://dx.doi.org/10.1177/0022042615619642
Walden University. (2021, August 24). Strengthen your stats skills: Confidence Intervals [Video]. YouTube. https://www.youtube.com/watch?v=XLTwPfLlQKg&list=PLNgQgQNniJ27hx9BxttFaeQMZhkB3sOPB&index=5
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