Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you
Increase the confidence level,
When the confidence level is increased, the critical value also increases. For this reason, the confidence interval widens. Wider confidence interval is important and it shows increased confidence that population mean lies inside it ( Stock, & Watson, 2012) . In other terms, the increase in confidence level increases the z(α/2) value which in turn leads to an increase in standard error (z*s/√n).
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Increase the sample size
When the sample size is increased, the confidence interval narrows. When the sample size is increased, there will be a reduction in in the size of the width of the confidence interval. Usually sample sizes affect the standard errors. A large sample size reduces the standard error while a lower sample size increases the standard error. The square root of the sample size in the formula is usually the denominator, thus the outcome to standard error. Thus, smaller sample size reduces the confidence interval. An example is when you increase the sample size by 4 would be similar to multiplying the standard error by ½; hence, there will be a wider interval.
Increase the margin of error
Margin error is derived from formula [critical value*(standard deviation/sample size). The confidence interval is calculated by adding or subtracting the margin error to sample mean. Thus, an increase in margin error will lead to widening of the confidence interval. When the original sample statistic is increased, there will be an increase in the confidence level midpoint. Also, the margin error is affected by the sample size (Owen et al. 2010). Thus, margin error increases with an increase in population size. Margin error therefore increases the confidence interval level.
References
Owen, A. M., Hampshire, A., Grahn, J. A., Stenton, R., Dajani, S., Burns, A. S., ... & Ballard, C. G. (2010). Putting brain training to the test. Nature , 465 (7299), 775.
Stock, J. H., & Watson, M. W. (2012). Introduction to econometrics: Global edition . Boston, MA: Pearson Education.
