Confidence Interval Estimation for Mean and Proportion

# Basic Concepts:

• Confidence interval (or interval estimate) is a range of values determined from sample data, used to estimate the true value of a population parameter.

• Point estimate is a single value calculated from the sample data to estimate the parameter of interest.

• Confidence level, denoted by 1-alpha=gamma, represents the probability that the confidence interval contains the true value of the parameter.

• Standard error is the standard deviation of the point estimate, reflecting the accuracy of the estimate.

• Critical value is a value determined based on the sampling distribution of the point estimate and the confidence level, used to construct the confidence interval.

# Applications for Population Mean:

• If the population standard deviation (sigma) is known, the normal distribution should be used to construct the confidence interval.

• If the population standard deviation (sigma) is unknown, the Student t-distribution should be used to construct the confidence interval.

• Degrees of freedom for the Student t-distribution are calculated as n-1, where n is the sample size.

# Conclusion:

Confidence interval estimation is a valuable tool for estimating the true value of a population parameter based on sample data. Selecting the appropriate distribution for constructing the confidence interval depends on whether the population standard deviation is known or unknown.