7.6: Chapter 7 - Key Terms and Symbols
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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