Statistics I
Course Number: MTH 243
Transcript Title: Statistics I
Created: September 1, 2012
Updated: June 7, 2017
Total Credits: 5
Lecture Hours: 50
Lecture / Lab Hours: 0
Lab Hours: 0
Satisfies Cultural Literacy requirement: No
Satisfies General Education requirement: Yes
Grading options: A-F (default), P-NP, audit
Repeats available for credit: 0
Prerequisites
Prerequisite / Concurrent
Course Description
Introduces displaying data with graphs, numerical descriptions of data, producing data, elementary probability, probability distributions, confidence intervals and significance testing. Investigates applications from science, business, and social science perspectives. Graphing calculator required. Prerequisite: MTH 95. Prerequisite/concurrent: WR 121. Audit available.
Intended Outcomes
Upon successful completion of this course, students will be able to:
- Identify concepts and techniques from descriptive and inferential statistics and real-world applications of the same.
- Use concepts and techniques from descriptive and inferential statistics to describe, model, and analyze real-world problems.
- Critique the application of probability and statistics to real-world problems and effectively communicate these ideas in written and verbal form.
Alignment with Institutional Core Learning Outcomes
In-depth | 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication) |
In-depth |
2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving) |
3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy) | |
Not Addressed |
4. Appreciate cultural diversity and constructively address issues that arise out of cultural differences in the workplace and community. (Cultural Awareness) |
Minimally |
5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility) |
Outcome Assessment Strategies
Assessment shall include some combination of the following:
- Class participation
- Group projects
- Presentations
- Portfolios
- Research papers
- Homework assignments
- Written paper
- Quizzes
- Exams
- Other assessments of the instructors choosing
Course Activities and Design
Concepts will be introduced using lecture, group activities, calculator and/or computer programs, and computer laboratory explorations. Students will communicate their results orally and in writing.
Course Content (Themes, Concepts, Issues and Skills)
1.0 Introduction
The instructional goal is to explore how an understanding of statistics is beneficial to jobs in business, industry, government, medicine, and other fields.
1.1 Describe and discuss descriptive and inferential statistics.
1.2 Identify and describe common statistical terminology:
1.2.1 Population
1.2.2 Sample
1.2.3 Variable
1.2.4 Statistical inference
2.0 Describing Sets of Data
The instructional goal is to explore, analyze, and describe a set of data using graphical and numerical methods.
2.1 Identify qualitative and quantitative data.
2.2 Construct pie charts and bar charts.
2.3 Construct frequency and relative frequency distributions.
2.4 Construct frequency and relative frequency histograms.
2.5 Construct a stem-and-leaf display.
2.6 Construct a dotplot.
2.7 Describe the shape of a distribution as symmetric, skewed left, or skewed right.
2.8 Calculate and interpret the numerical measures of central tendency:
2.8.1 Mean
2.8.2 Median
2.8.3 Mode
2.9 Calculate and interpret the numerical measures of dispersion:
2.9.1 Range
2.9.2 Variance
2.9.3 Standard deviation
2.10 Interpret the meaning of the standard deviation using the Empirical Rule and/or Chebyshev’s Rule.
2.11 Calculate and interpret measures of relative standing:
2.11.1 Percentile ranking
2.11.2 Z-scores
2.12 Construct a modified boxplot.
2.13 Look for relationships between two variables:
2.13.1 Identify response and explanatory variables.
2.13.2 Construct a scatterplot.
2.13.3 Determine whether the two variables have a positive or negative association.
2.13.4 Calculate and interpret the correlation coefficient, r, and the coefficient of determination, r2.
2.13.5 Calculate and interpret the least-squares regression line.
2.13.6 Predict values of the dependent variable using the least-squares regression line.
2.13.7 Discuss cautions about regression and correlation including:
2.13.7.1 Residuals
2.13.7.2 Lurking variables
2.13.7.3 Causation
2.14 Using technology
2.14.1 Input and edit data
2.14.2 Draw dotplots, histograms, boxplots, scatterplots, and residual plots.
2.14.3 Calculate one-variable summary statistics.
3.0 Producing Data
The instructional goal is to explore the design of statistical samples and experiments.
3.1 Identify the elements of experiments and observational studies including:
3.1.1 Experimental units
3.1.2 Factors
3.1.3 Placebo
3.1.4 Bias
3.1.5 Randomization
3.2 Identify the differences between experiments and observational studies.
3.3 Identify sample designs including:
3.3.1 Voluntary response sample
3.3.2 Simple random sample
3.3.3 Stratified sample
3.3.4 Multistage sample
3.3.5 Systematic sample
3.3.6 Cluster sample
3.4 Using technology or a table of random numbers select a simple random sample.
4.0 Elementary Probability
The instructional goal is to explore the concepts of probability.
4.1 Identify and describe standard probability terms:
4.1.1 Experiment
4.1.2 Simple event
4.1.3 Sample space
4.1.4 Disjoint events
4.1.5 Independent events
4.1.6 Complementary events
4.2 Calculate and interpret marginal, joint, and conditional probabilities.
4.3 Calculate and interpret probabilities using:
4.3.1 Venn diagrams
4.3.2 Contingency tables
4.3.3 Tree diagrams
4.3.4 Additive rule
4.3.5 Multiplicative rule
4.4 Calculate and interpret probabilities using Bayes’ Theorem.
5.0 Random Variables and Probability Distributions
The instructional goal is to explore and analyze various random variables and probability distributions.
5.1 Identify and describe terminology:
5.1.1 Random variable
5.1.2 Probability distribution
5.1.3 Expected value
5.1.4 Variance and standard deviation
5.1.5 Probability density function
5.2 Identify a random variable as discrete or continuous.
5.3 Explore the binomial discrete probability distribution.
5.4 Explore the normal continuous probability distribution.
5.5 Approximate a binomial probability using a normal distribution.
5.6 Using technology, input a probability density function and its appropriate parameters.
5.6.1 Compute and interpret the probability that a discrete random variable is equal to a specified value.
5.6.2 Compute and interpret the probability that a discrete random variable lies within an interval of values.
5.6.3 Compute and interpret the probability that a continuous random variable lies within an interval of values.
5.7 Using technology, simulate probability distributions by generating random data.
5.7.1 Binomial
5.7.2 Normal
5.8 Compute and interpret the mean and standard deviation of:
5.8.1 A discrete random variable
5.8.2 A linear transformation of a random variable
5.8.3 The sum or difference of two independent random variables
6.0 Sampling Distributions
The instructional goal is to explore and analyze sampling distributions.
6.1 Identify and describe terminology:
6.1.1 Parameter
6.1.2 Statistic
6.1.3 Point estimator
6.1.4 Biased vs. unbiased
6.2 Calculate and interpret a sample mean and its standard deviation.
6.3 Explore the distribution of the means of samples drawn from a population.
6.4 Identify the properties of sampling distributions.
6.5 Explore the Central Limit Theorem.
6.6 Solve probability problems involving the standardized sample mean.
7.0 Estimation
The instructional goal is to estimate a population parameter by calculating a confidence interval.
7.1 Identify and describe terminology:
7.1.1 Point estimator
7.1.2 Confidence level
7.1.3 Confidence interval
7.2 Calculate and interpret a large-sample estimation of a population mean or proportion.
7.3 Calculate a sample size to attain a desired margin of error and confidence level.
8.0 Significance Testing
The instructional goal is to understand the logic, formal structure, appropriate use, and proper interpretation of significance testing.
8.1 Identify and describe terminology:
8.1.1 Null hypothesis (as an equation)
8.1.2 Alternative hypothesis (one-sided vs two-sided)
8.1.3 Significance level (alpha-value)
8.1.4 P-value
8.1.5 Statistical significance
8.2 Performance and interpretation:
8.2.1 Specify an appropriate parameter of interest
8.2.2 Identify/produce data, and properly set up a basic significance test
8.2.3 Be able to compute a P-value:
(a) Using a single (context-specific) significance test software function and/or
(b) Using a calculated test statistic and a software Cdf function, and/or
(c) Using a normal distribution table.
8.2.4 Assess results for statistical significance against a predetermined significance level.
8.2.5 Distinguish between statistical vs. practical significance.
8.3 Compare the information a confidence interval provides versus a significance test.
8.4 Verify required conditions for the test of significance.
Department Notes
This is the first term of a two-term sequence (MTH 243 and 244). This course is intended to provide an introduction to statistics in a data-based setting.