Confidence Intervals for Population Mean and Proportion
What is Confidence Interval?
Confidence interval refers to the range that is calculated for a population parameter, such as a mean, with a specified level of confidence that a particular value belongs to the population.
How to Find the Confidence Interval for the Population Mean?
Confidence interval for population mean is calculated using the steps added below:
Step 1: Find confidence level with appropriate z*-value.
Step 2: Find the sample mean (x̄) for the sample size (n).
Step 3: Find product of z* times σ and divide that result by square root of n.
What is the 95% Confidence Interval for the Population Mean Difference?
95% confidence interval on the difference between means that population mean extends from -4.267 to 0.267.
What meaning does Confidence Level Attribute to?
Confidence level indicates the possibility that the confidence interval covers the whole true population. Sometimes these levels are 90, 95, or 99 percent.
What is Effect of Factors on Width of a Confidence Interval?
Width of the confidence interval is a factor of the size of the sample and the confidence level. Increased number of samples and smaller confidence level lead to a shorter interval.
Do Confidence Intervals Exist Always?
Confidence Interval are often not even, for instance, due to the misleading or skewed data or small symbols. They tend to be relatively smooth and symmetric when the sample is large as a result of Central Limit Theorem.
Confidence Intervals for Population Mean and Proportion
Confidence intervals for population mean estimate the range within which the true mean lies, based on sample data. For proportions, they estimate the range within which the true population proportion lies. Both intervals reflect statistical certainty about the estimates.
This article explains confidence intervals, their calculation, interpretation, and applications for population means and proportions in statistics.
Table of Content
- Defining Confidence Interval
- Formula for Confidence Interval
- Confidence Interval Table
- Calculating Confidence Interval
- Example of Confidence Interval Calculation