UVU Math 1040 Course Objectives

Introduction to Statistics Course Objectives

1. Interpret and represent mathematical information using symbolic, visual, numerical and verbal conventions. This will be addressed through graphical methods of data representation.
2. Solve problems using numeric, algebraic, geometric and statistical methods. This will be addressed through calculating probabilities and confidence intervals.
3. Use quantitative information in context, and determine reasonableness of results. This will be addressed through interpretation of hypothesis test results, the difference between statistical significance and practical significance, and comparisons between observational and experimental studies.
4. Use appropriate mathematical tools in problem solving (e.g. calculators, computers, measurement instruments and manipulatives). This will be addressed through instruction on the statistical capabilities of a TI-84 calculator and excel.

Description

A quantitative literacy course with a statistical theme. Includes descriptive statistics, sampling, and inferential methods. Emphasizes problem solving and critical thinking.

Producing Data

A student should be able to:

1. Identify types of data:  numerical and categorical
2. Distinguish between populations vs. samples, and parameters vs. statistics
3. Identify types of bias in sampling such as convenience sampling, volunteer sampling, non-response bias, and others
4. Conduct simple random samples and compute 95% confidence intervals.
5. Distinguish between observational studies and randomized comparative experiments
6. Explain the logic of experimental design and statistical significance
7. Know the Institutional Review Board process including informed consent and confidentiality and anonymity.
8. Know measurement concepts such as reliability, validity, and predictive validity.
9. Check numbers for reasonableness and plausibility.

Organizing Data

A student should be able to:

1. Construct graphs for distributions of both numerical and categorical variables.
3. Compute the mean and sample standard deviation for numerical data sets.
4. Compute the five number summary and construct a boxplot for numerical data sets.
5. Compute percentiles and probabilities for the normal distribution using both the z-transformation and the “68-95-99.7” rule.
6. Describe relationships between two numerical variables using scatterplots, correlation, linear regression and prediction.
7. Understand the consumer price index and government statistics.

Chance

A student should be able to:

1. Understand probability and myths about chance behavior.
2. Know properties of probability models
3. Compute probabilities for the sample proportions using z-transformations.
4. Conduct simulations using probability models and tree diagrams.
5. Know and be able to compute the house edge with expected values and the law of large numbers.

Inference

A student should be able to:

1. Compute confidence intervals for a population mean or population proportion.
2. Compute probabilities for the sample mean using the central limit theorem and z-transformations.
3. Conduct hypothesis tests for the population mean or proportion, using the traditional five step process.
4. Interpret p-values and statistical significance.
5. Understand the use and abuse of statistical inference.
6. Analyze relationships between two categorical variables using two-way tables and the Chi-Square Test.