Designed as a first course for students in business administration, education, social sciences, engineering, and other fields in which data are collected and predictions are made. Covers descriptive measures, the summarizing of data, an introduction to probability, discrete probability distributions, normal probability distributions, sampling distributions, estimation, confidence intervals, hypothesis testing, correlation, regression, chi square tests, one-way analysis of variance (ANOVA), and use of nonparametric tests. In addition, utilizes a statistical software package to conduct data analysis and solve applied problems. Requires a graphing calculator, with the TI-84 Plus series recommended. Also requires access to an online homework management system as well as a statistical software package.
Goals, Topics, and Objectives
- To introduce students to the fundamental concepts of probability.
- To present the basic techniques used in descriptive and inferential statistics.
- To introduce students to the use of technology for data exploration and analysis.
- To encourage students to communicate effectively in presenting the results of a statistical study.
- Data Types
- Distinguish between a population and a sample, between a parameter and a statistic, and between descriptive and inferential statistics.
- Distinguish between qualitative data and quantitative data.
- Classify data with respect to the four levels of measurement.
- Identify the different types of sampling techniques.
- Descriptive Statistics
- Construct frequency distributions, frequency histograms, frequency polygons, relative frequency histograms, stem-and-leaf, and box-and-whisker plots.
- Find and interpret the mean, median, and mode of a population and of a sample.
- Find and interpret the range, variance, and standard deviation of a population and of a sample.
- Interpret standard deviation by means of the Empirical Rule and Chebychev’s theorem.
- Find and interpret quartiles, percentiles and interquartile range of data set.
- Find and interpret the standard score (z-score).
- Identify the sample space of a probability experiment and identify simple events.
- Distinguish between classical, empirical, and subjective types of probability.
- Distinguish between dependent and independent events.
- Determine if two events are mutually exclusive.
- Calculate probabilities through the use of the Complement Rule, the Multiplication Rule, and the Addition Rule.
- Discrete Probability Distributions
- Distinguish between discrete random variables and continuous random variables.
- Construct a discrete probability distribution and its graph.
- Determine if a function is a probability distribution, and find the mean, standard deviation, and expected value of the distribution.
- Find binomial probabilities using the binomial probability formula.
- Find the mean and standard deviation of a binomial probability distribution.
- Normal Probability Distributions
- Find probabilities for normal distributions using both tables and technology.
- Find specific data values of a normal distribution associated with a given probability using both tables and technology.
- Verify the properties of sampling distributions.
- Apply the Central Limit Theorem to find the probabilities associated with sample means.
- Confidence Intervals
- Construct and interpret confidence intervals for a population mean using both small and large sample techniques by means of tables and technology.
- Construct and interpret confidence intervals for a population proportion by means of tables and technology.
- Construct and interpret confidence intervals for for the difference of proportions or means for two populations.
- Determine the minimum sample size required when estimating the population mean and population proportion.
- Construct and interpret confidence intervals for the population variance and standard deviation by means of both tables and technology.
- Hypothesis Testing Using a Simple Sample
- Conduct and present formal hypothesis tests involving the mean of a population using both small and large sample techniques.
- Conduct and present formal hypothesis tests involving a population proportion.
- Conduct and present formal hypothesis tests involving the standard deviation (or variance) of a population using a sample drawn from a normal population.
- Hypothesis Testing with Two Samples
- Conduct and present a hypothesis test for the difference between two population means using techniques for large independent samples, small independent samples, and dependent samples.
- Conduct and present a hypothesis test for the difference between two population proportions.
- Correlation and Regression
- Determine the coefficient of correlation for a sample of bivariate data by means of technology and interpret the value in the context of the data.
- Conduct and present a hypothesis test for the significance of a population correlation coefficient.
- Determine the equation of a regression line for bivariate data by means of technology and use the equation to make predictions.
- Determine the coefficient of determination for a sample of bivariate data by means of technology and interpret the value in the context of the data.
- Chi-Square Tests and the F-Distribution
- Test whether a frequency distribution fits a claimed distribution through use of the chi-square distribution.
- Test whether two variables are independent by means of contingency tables and the chi-square distribution.
- Perform a two-sample F-test to compare two variances.
- Test claims involving three or more means through use of one-way-analysis of variance (ANOVA).
- Nonparametric Tests
- Test a population median and the difference between two population medians through use of the nonparametric Sign Test.
- Determine if two samples (both independent and dependent) are selected from populations with the same distribution through use of the nonparametric Wilcoxon Tests.
- Determine if three or more samples were selected from populations with the same distribution through use of the Kruskal-Wallis Test.
Course Alignment to the RM@RT Learning Outcomes in Statistics
The above course topics and objectives are aligned to meet the recommended learning outcomes by the RM@RT Statistics Working Group
The recommended learning outcomes are listed below
Introductory Statistics Essential Outcomes:
- Demonstrate understanding of the basic principles of data collection, observational study, and experimental design. This may include (but is not limited to) topics such as randomness, sampling error, sampling techniques, bias, blinding, and types of data.
- Construct and interpret graphical and tabular displays of univariate data. These displays may include (but are not limited to): frequency distributions, pie charts, boxplots, stem plots, histograms.
- Summarize distributions of univariate data using measures of central tendency, measures of dispersion, and measures of location.
- Compare multiple data sets with graphical displays and numerical measures.
- Perform basic probability computations. These may include (but are not limited to): the addition rule, the multiplication rule for independent events, and the complement rule.
- Solve problems by applying appropriate probability distributions, which may include (but are not limited to) discrete, binomial, and normal probability distributions.
- Use the Central Limit Theorem to model sampling distributions and compute probabilities based on sampling distributions.
- Analyze bivariate quantitative data. This includes (but is not limited to), generating and interpreting r- and, r^2-values, scatterplots, and the least- squares regression lines for bivariate data.
- Construct and interpret confidence intervals of proportion or mean for one population.
- Construct and interpret confidence intervals for the difference of proportions or means for two populations.
- Perform hypothesis tests for the means and proportions for one population. This includes interpreting p-value, type I and type II errors, and statistical and practical significance.
- Perform hypothesis tests for the difference of proportions or means for two populations. This includes interpreting p-value, type I and type II errors, and statistical and practical significance.
- Interpret and apply output from a statistical software package and/or a graphing utility.
- Interpret and apply appropriate statistical techniques and concepts to real-life data and situations in order to make decisions and/or draw conclusions.
Introductory Statistics Optional Outcomes:
- Perform intermediate probability computations. These may include (but are not limited to): the multiplication rule for dependent events, conditional probability, and Bayes Theorem.
- Analyze bivariate qualitative data presented in two-way tables and interpret relationships between categorical variables. This may include (but is not limited to) computing probabilities, identifying lurking variables, explaining Simpson’s Paradox, and conducting appropriate chi-square tests.
- Perform more advanced hypothesis tests such as the goodness-of-fit test, independence test, and ANOVA.
Assessment and Requirements
- A comprehensive final examination, weighted in a manner that is worth at least (15%) of the final course grade, is required of all sections. In selected semesters this exam may be a common exam administered to all sections of Math 141.
- All students will be required to complete online homework. This online homework must be weighted in such a manner so that it is worth between six percent (6%) and twelve percent (12%) of the final course grade.
- Additional assessment of student achievement may include assignments, quizzes, and exams.
- Application problems must not only be included on chapter exams but also on the final exam.
- A graphing calculator is required of each student and the Mathematics Department recommends and uses the TI-84 Series.
- Access to an online homework management system is required.
- Access to a statistical software package is required.
- Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.
Credit for Prior College-Level Learning
Minimum score of 3, Advanced Placement (AP) Statistics exam