Statistics

Sampling and Data

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables and the Normal Distribution

Central Limit Theorem

Confidence Intervals

Hypothesis Testing

Regression Correlation

Understand the investigative process of statistics and differentiate between descriptive and inferential statistics.

Differentiate between a population and a sample.

Construct a simple random sample.

Understand the differences between stratified sampling, cluster sampling, systematic sampling, and convenience sampling.

Determine when samples of convenience are acceptable and how sampling bias and error can occur.

Identify and classify data as either qualitative or quantitative and classify quantitative data as either discrete or continuous data.

Display and interpret qualitative data with graphs: pie graphs, bar graphs, and pareto charts.

Differentiate between levels of measurement: nominal, ordinal, interval, and ratio.

Create a frequency distribution from a list of quantitative and/or qualitative data.

Calculate relative frequencies and cumulative frequencies using a frequency distribution table.

Understand differences between a designed experiment and an observational study.

Differentiate between the types of variables used in a designed experiment.

Understand different methods used in an experiment to isolate effects of the explanatory variable.

Display and interpret graphs using quantitative data including stem-and-leaf plots, line graphs, and box plots.

Construct a histogram from a frequency distribution table.

Interpret data using histograms and time series graphs.

Analyze a frequency distribution table and determine the sample size, class width and class midpoints.

Recognize, describe, and calculate the measures of locations of data: quartiles, median, five number summary, interquartile range outliers, upper and lower fences, and percentiles.

Distinguish between a parameter and a statistic.

Calculate and differentiate between different measures of center: mean, median, and mode.

Calculate the mean of a frequency distribution: GPA and weighted grade.

Interpret the shape of the distribution from a graph: normal/symmetric, skewed, or uniform.

Calculate and differentiate between different measures of spread: range, variance, and standard deviation.

Determine if a data value is unusual based on standard deviations, μ ± 2σ.

Understand and use terminology and symbols of probability.

List the elements of events and the sample space from an experiment.

Understand the concept of randomness: flipping a coin, rolling a die, and drawing a card from a standard 52 card deck.

Differentiate between and calculate different types of probabilities: empirical and theoretical.

Explain the Law of Large Numbers.

Calculate and interpret probabilities using the complement rule, addition rule, and multiplication rule.

Differentiate between and calculate probabilities for different types of events: independent, dependent, with or without replacement, conditional, and mutually exclusive.

Use Venn diagrams and lists to solve probability problems when appropriate.

Identify the random variable in a probability experiment.

Recognize and understand discrete probability distribution functions.

Create a probability distribution for the values of a discrete random variable.

Use a probability function to determine probabilities associated with a discrete random variable.

Calculate and interpret the mean (expected value), variance, and standard deviation for discrete random variables and binomial probability distributions.

Determine when a probability distribution should be classified as a discrete binomial probability distribution, and calculate probabilities associated with such a distribution.

Recognize and understand continuous probability density functions.

Use a probability density curve to describe a population, including a normal population.

Calculate and interpret the area under a probability density curve.

Calculate and interpret a z-score, understanding the concept of "standardizing" data.

Calculate and interpret z-scores using the Empirical Rule, understanding the general properties of the normal distribution: 100% is the total area under the curve, exactly 50% is to the left and right of the mean, and it is perfectly symmetric about the mean.

Use technology to calculate the area under the curve for any normal distribution model: left, right, and between.

Use technology to calculate percentiles, quartiles, and other numerical values of X for a specified area under a normal curve, including unusual values (P(X) < 5% and μ ± 2σ).

Recognize the characteristics of the mean of sample means taken from different types of populations: normal and non-normal.

Calculate the mean of sample means taken from different types of populations: normal and non-normal.

Describe how the means of samples calculated from a non-normal population might be distributed.

Apply the Central Limit Theorem to normal and non-normal populations and compute probabilities of a sample mean.

Determine whether the Central Limit Theorem can be used for a given situation.

Assess the impact of sample size on sampling variability.

Read and write confidence intervals using two different forms: point estimate plus/or minus margin of error (error bound) and interval notation.

Calculate and interpret confidence intervals for estimating a population mean and a population proportion.

Calculate the margin of error (error bound) using sample statistics.

Predict if a confidence interval will become wider or narrower given larger or smaller sample sizes as well as higher or lower confidence levels.

Find the point estimate and margin of error (error bound) when given a confidence interval.

Estimate the sample size necessary to estimate a population mean.

Recognize the difference between the sample mean, <img src="http://purl.org/ASN/resources/images/D21321918/TN_Math_2023_S7g.gif"/> and the population mean, μ, as well as the difference between the sample standard deviation, <em>s</em>, and standard error of the mean, s/√n.

Find critical values for Z_α/2 and t_α/2 given a value of α and degrees of freedom.

Estimate the sample size necessary to estimate a population proportion.

Determine the appropriate null and alternative hypotheses when presented with a problem.

Differentiate between Type I and Type II errors.

Understand and list the assumptions needed to conduct z-tests and t-tests.

Determine whether to reject or fail to reject the null hypothesis using the p-value method.

Determine if a test is left-tailed, right-tailed, or two-tailed.

Differentiate between independent group and matched pair sampling.

Calculate test statistics and p-values for hypotheses tests: single proportion, single mean, and difference between two means.

Conduct hypotheses tests for a single proportion and a single mean.

Test hypotheses regarding the difference of two independent means (assume the variances are not pooled).

Draw conclusions and make inferences about claims based on hypotheses tests.

Differentiate between the independent (explanatory variable, x) and the dependent (response variable, y) in a bivariate data set.

Create a scatter plot and determine the type of relationship that exists between two variables: positive or negative correlation and weak or strong correlation.

Calculate and interpret the correlation coefficient using technology.

Calculate the line of best fit and interpret the coefficient of determination.

Use the line of best fit to make conclusions about the relationship between two variables, understanding correlation does not imply causation.

Calculate a residual using the line of best fit.

Use the p-value to determine if a line of best fit is statistically significant.

For a given value of x, find the appropriate estimated value of y.

Distinguish between interpolated and extrapolated values and explain why interpolated values are more reliable.

Perform a residual analysis to check assumptions of regression.