## Statistics - Mathematics - Texas

### Standards: TEKS

Stat.1: Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(a) apply mathematics to problems arising in everyday life, society, and the workplace;
(b) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
(c) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
(d) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
(e) create and use representations to organize, record, and communicate mathematical ideas;
(f) analyze mathematical relationships to connect and communicate mathematical ideas; and
(g) display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Stat.2: Statistical process sampling and experimentation. The student applies mathematical processes to apply understandings about statistical studies, surveys, and experiments to design and conduct a study and use graphical, numerical, and analytical techniques to communicate the results of the study. The student is expected to:
(a) compare and contrast the benefits of different sampling techniques, including random sampling and convenience sampling methods;
(b) distinguish among observational studies, surveys, and experiments;
(c) analyze generalizations made from observational studies, surveys, and experiments;
(d) distinguish between sample statistics and population parameters;
(e) formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions;
(f) communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation; and
(g) critically analyze published findings for appropriateness of study design implemented, sampling methods used, or the statistics applied.

Stat.3: Variability. The student applies the mathematical process standards when describing and modeling variability. The student is expected to:
(a) distinguish between mathematical models and statistical models;
(b) construct a statistical model to describe variability around the structure of a mathematical model for a given situation;
(c) distinguish among different sources of variability, including measurement, natural, induced, and sampling variability; and
(d) describe and model variability using population and sampling distributions.

Stat.4: Categorical and quantitative data. The student applies the mathematical process standards to represent and analyze both categorical and quantitative data. The student is expected to:
(a) distinguish between categorical and quantitative data;
(b) represent and summarize data and justify the representation;
(c) analyze the distribution characteristics of quantitative data, including determining the possible existence and impact of outliers;
(d) compare and contrast different graphical or visual representations given the same data set;
(e) compare and contrast meaningful information derived from summary statistics given a data set; and
(f) analyze categorical data, including determining marginal and conditional distributions, using two-way tables.

Stat.5: Probability and random variables. The student applies the mathematical process standards to connect probability and statistics. The student is expected to:
(a) determine probabilities, including the use of a two-way table;
(b) describe the relationship between theoretical and empirical probabilities using the Law of Large Numbers;
(c) construct a distribution based on a technology-generated simulation or collected samples for a discrete random variable; and
(d) compare statistical measures such as sample mean and standard deviation from a technology-simulated sampling distribution to the theoretical sampling distribution.

Stat.6: Inference. The student applies the mathematical process standards to make inferences and justify conclusions from statistical studies. The student is expected to:
(a) explain how a sample statistic and a confidence level are used in the construction of a confidence interval;
(b) explain how changes in the sample size, confidence level, and standard deviation affect the margin of error of a confidence interval;
(c) calculate a confidence interval for the mean of a normally distributed population with a known standard deviation;
(d) calculate a confidence interval for a population proportion;
(e) interpret confidence intervals for a population parameter, including confidence intervals from media or statistical reports;
(f) explain how a sample statistic provides evidence against a claim about a population parameter when using a hypothesis test;
(g) construct null and alternative hypothesis statements about a population parameter;
(h) explain the meaning of the p-value in relation to the significance level in providing evidence to reject or fail to reject the null hypothesis in the context of the situation;
(i) interpret the results of a hypothesis test using technology-generated results such as large sample tests for proportion, mean, difference between two proportions, and difference between two independent means; and
(j) describe the potential impact of Type I and Type II Errors.

Stat.7: Bivariate data. The student applies the mathematical process standards to analyze relationships among bivariate quantitative data. The student is expected to:
(a) analyze scatterplots for patterns, linearity, outliers, and influential points;
(b) transform a linear parent function to determine a line of best fit;
(c) compare different linear models for the same set of data to determine best fit, including discussions about error;
(d) compare different methods for determining best fit, including median-median and absolute value;
(e) describe the relationship between influential points and lines of best fit using dynamic graphing technology; and
(f) identify and interpret the reasonableness of attributes of lines of best fit within the context, including slope and y-intercept.