What is Confidence Interval? Is it better to have a large Confidence Interval or a small Confidence Interval? Briefly explain.
A confidence interval is a statistical range that estimates the true value of a population parameter, such as a mean or proportion. It provides a measure of uncertainty by specifying a lower and upper bound within which the true value is likely to fall.
To calculate a confidence interval, you usually need three components: the sample statistic (e.g., sample mean or proportion), the standard deviation or standard error, and the desired level of confidence (usually expressed as a percentage, such as 95% or 99%).
Now, to answer your second question, it is generally better to have a smaller confidence interval. A smaller interval indicates a more precise estimate of the population parameter, meaning that we have a higher level of confidence that the true value lies within a narrower range.
However, it is important to note that the size of the confidence interval is influenced by several factors. Firstly, the sample size: larger sample sizes tend to result in smaller confidence intervals as they provide more accurate estimates of the population parameter. Secondly, the variability in the data: if the data points are spread out from the mean, the confidence interval may be wider.
Choosing the appropriate width of the confidence interval involves a trade-off between precision and the level of confidence desired. Higher confidence levels (e.g., 99%) will result in wider intervals, as they require a greater degree of certainty. On the other hand, lower confidence levels (e.g., 90%) will produce narrower intervals, but with reduced certainty.
Ultimately, the choice of confidence interval width depends on the specific research question, available data, and the level of confidence required by the researcher or decision-maker.