Statistics I

Course Number: MTH 243
Transcript Title: Statistics I
Created: September 1, 2012
Updated: August 15, 2019
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:

  1. Identify concepts and techniques from descriptive and inferential statistics and real-world applications of the same.
  2. Use concepts and techniques from descriptive and inferential statistics to describe, model, and analyze real-world problems.
  3. 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

Major 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)

Major

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

Major

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. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)

Major

5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Core Learning Outcomes (CLOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

Major Designation

  1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
  2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
    • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Minor Designation

  1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
  2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
    • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

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

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

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.