"In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter."
An interval estimate of a population parameter with a level of confidence.
Probability Distributions: These are mathematical models that help to describe and predict the behavior of random variables. Understanding the properties of probability distributions is essential for building confidence intervals.
Normal Distribution: This is a type of probability distribution that is commonly used in statistics. It has a symmetrical bell-shaped curve and is characterized by two parameters: The mean and the standard deviation.
Central Limit Theorem: This theorem states that for a large enough sample size, the distribution of sample means will approximate a normal distribution, regardless of the population distribution.
Confidence Intervals: These are numerical ranges that estimate the true value of a population parameter with a specified level of confidence.
z-Score: This is a standardized score that measures how many standard deviations a data point is from the mean.
Margin of Error: This is the amount by which the upper and lower bounds of a confidence interval vary from the sample mean.
Sample Size: This refers to the number of observations in a sample. The larger the sample size, the more accurate the confidence interval will be.
Level of Confidence: This refers to the degree of certainty that the true population parameter falls within the confidence interval. The most common level of confidence used is 95%.
Hypothesis Testing: This is a statistical method used to determine whether an observed difference between two groups is statistically significant or due to chance.
T-Distribution: This is a probability distribution used to calculate confidence intervals and perform hypothesis tests when the sample size is small or the population standard deviation is unknown.
Interval Estimation: This is the process of estimating an unknown population parameter using a sample statistic and a confidence interval.
Significance Testing: This is the statistical analysis used to determine whether a research hypothesis is supported by the data or not.
Confidence Interval Widths: This refers to the range between the upper and lower bounds of a confidence interval. Narrower intervals provide more precise estimates of population parameters.
Statistical Error: This refers to the difference between the observed value and the true value of the population parameter. Confidence intervals attempt to minimize this error.
One-sample z-interval: Used to estimate the population mean when the population standard deviation is known.
One-sample t-interval: Used to estimate the population mean when the population standard deviation is unknown.
Two-sample z-interval: Used to estimate the difference between two population means when the populations are normally distributed and the population standard deviation is known.
Two-sample t-interval: Used to estimate the difference between two population means when the populations are normally distributed and the population standard deviation is unknown.
Proportion Confidence Interval using z-statistic: Used to estimate the population proportion.
Proportion Confidence Interval using t-statistic: Used to estimate the population proportion when the sample size is small or the population is not normally distributed.
Confidence interval for the difference in proportions: Used to estimate the difference between two population proportions.
Confidence interval for the ratio of variances: Used to estimate the ratio of two population variances.
Confidence interval for the difference in means for paired samples: Used to estimate the difference between two populations that are paired, for example, before and after measurements of the same variable.
Bootstrap confidence interval: A non-parametric method that does not require any assumptions about the population distribution. It involves resampling the data to estimate the sampling distribution.
Bayesian confidence interval: Used in Bayesian statistics to estimate the credible interval of the parameter of interest. The credible interval is the range of values within which the true value of the parameter is believed to lie with a certain probability.
"A confidence interval is computed to estimate an unknown parameter."
"The confidence level determines the range of values in a confidence interval."
"The 95% confidence level is most common."
"No, other levels such as 90% or 99% are sometimes used."
"The degree of confidence or confidence coefficient represents the long-run proportion of CIs that theoretically contain the true value of the parameter."
"The confidence level represents the proportion of CIs that should contain the parameter's true value."
"The nominal coverage probability is tantamount to the proportion of CIs that should contain the true value of the parameter."
"All else being the same, a larger sample produces a narrower confidence interval."
"Greater variability in the sample produces a wider confidence interval."
"A higher confidence level produces a wider confidence interval."
"Out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value."
"No, the sample size does not affect the confidence level."
"The sample size, variability in the sample, and the confidence level affect the width of the CI."
"A larger sample size contributes to a narrower confidence interval."
"Greater variability in the sample contributes to a wider confidence interval."
"No, a higher confidence level actually leads to a wider confidence interval."
"The 95% confidence level is the most commonly used."
"Confidence intervals are theoretically accurate if they contain the true value of the parameter based on the confidence level."
"A confidence interval provides a range of estimates for an unknown parameter."