7.6: Chapter 7 - Key Terms and Symbols
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Glossary of Key Terms and Symbols
Key Terms
Confidence Interval: An interval estimate that gives a range of values likely to contain the population parameter with a certain level of confidence.
Confidence Level: The probability that the confidence interval contains the true population parameter; common levels are 90%, 95%, and 99%.
Margin of Error: The maximum expected difference between the point estimate and the actual population parameter; it reflects the precision of the estimate.
Point Estimate: A single value derived from sample data used to estimate a population parameter.
Population Mean: The average value of a characteristic for the entire population.
Population Proportion: The ratio of individuals in a population with a particular characteristic, expressed as a decimal or percent.
Proportion Complement: The value obtained by subtracting the sample or population proportion from 1; represents the opposite category.
Sample Mean: The average value of a characteristic in a sample, used as a point estimate for the population mean.
Sample Proportion: The ratio of individuals in a sample with a particular characteristic.
Sample Size: The number of observations or data points in a sample affects the accuracy and reliability of confidence intervals.
Sampling Distribution: The probability distribution of a statistic (like the sample mean or proportion) based on all possible random samples from a population.
Sampling Error: The difference between the sample statistic and the corresponding population parameter due to chance variation in sample selection.
Standard Error: A measure of the variability of a sampling distribution; it is used to construct confidence intervals.
t-Distribution: A probability distribution used instead of the normal distribution when estimating the population mean with a small sample size or when the population standard deviation is unknown.
z-Value (or z-Score): A value from the standard normal distribution used in constructing confidence intervals when the population standard deviation is known and the sample size is large.
Key Symbols
\( \bar{x} \) - sample mean.
\( \mu \) - population mean.
\( \hat{p} \) - sample proportion.
\( p \) - population proportion.
\( q \) - complement of the population proportion (i.e., \( q = 1 - p \)).
\( \hat{q} \) - complement of the sample proportion (i.e., \( \hat{q} = 1 - \hat{p} \)).
\( n \) - sample size.
\( E \) - margin of error.
\( \alpha \) - significance level (i.e., \( 1 - \) confidence level).
\( z_{\alpha/2} \) - critical value from the standard normal distribution.
\( t_{\alpha/2} \) - critical value from the t-distribution.
\( \sigma \) - population standard deviation.
\( s \) - sample standard deviation.
\( SE \) - standard error.
\( CI \) - confidence interval.
\( CL \) - confidence level.
Authors
"7.6: Chapter 7 - Key Terms and Symbols" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY 4.0