MAT-200 Statistics
This statistics course is designed for an experienced mathematics student. It is a one semester course covering descriptive and inferential statistics. Topics included are measures of center; measures of dispersion; hypothesis testing; estimations for population means, proportions, and variance; determination of sample size; uses of the Chi-square distribution; analysis of variance; linear correlation and linear regression; and statistical research. The course will emphasize computer or calculator use (graphing calculator, Minitab, Excel, StatCrunch, R, etc.) to obtain results. Simulation-based methods will be used to support and enhance traditional methods of inference. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.
Prerequisite
earn a C- or better in
MAT-145 or Placement into Math Level 3 or Higher
For more detailed course information view the
Course Outline
Course Description
This statistics course is designed for an experienced mathematics student. It is a one semester course covering descriptive and inferential statistics. Topics included are measures of center; measures of dispersion; hypothesis testing; estimations for population means, proportions, and variance; determination of sample size; uses of the Chi-square distribution; analysis of variance; linear correlation and linear regression; and statistical research. The course will emphasize computer or calculator use (graphing calculator, Minitab, Excel, StatCrunch, R, etc.) to obtain results. Simulation-based methods will be used to support and enhance traditional methods of inference. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.
Credit Hours
3Semester(s) Course Will Be Offered
Fall, Spring, Summer
Prerequisites
earn a C- or better in MAT-145 or Placement into Math Level 3 or Higher
SUNY General Education Course
- Mathematics and Quantitative Reasoning
First Year Experience Course
No
Course Learning Outcomes
- Analyze sample data, and interpret the results of statistical procedures.
- Apply probability distributions and sampling distributions to calculate probabilities.
- Use confidence intervals to estimate population parameters.
- Use hypothesis testing to evaluate claims.
- Apply simulation-based methods and normal theory models to make statistical inferences, recognizing the assumptions underlying each approach.
Topic Outline
- 1. Fundamental terminology and concepts
- a. Population vs. sample
- b. Parameter vs. statistic
- c. Variables
- d. Data: quantitative vs. qualitative, and discrete vs. continuous
- e. Sampling methods
- 2. Introduction to design of experiments
- a. Single-blind vs. double-blind
- b. Designs of experiments
- i. Randomized
- ii. Matched pairs
- iii. Randomized block
- 3. Computing and interpreting measures of central tendency and dispersion
- a. Mean and median
- b. Variance, standard deviation, and IQR
- 4. Probability distributions of random variables
- a. Random variables: discrete vs. continuous
- b. The concept of a probability distribution
- c. Representations of a probability distribution
- d. Computing the expected value of a probability distribution
- e. Binomial probability distribution
- i. Properties of a binomial experiment
- ii. Computing binomial probabilities
- iii. Computing the mean and standard deviation of a binomial probability distribution
- 5. Normal distribution
- a. Computing and interpreting the standard score (z-score)
- b. Empirical rule
- c. Techniques for identifying outliers
- d. Properties of a normal distribution
- e. Computing the probability of a random variable
- f. Calculating the value of a random variable from a proportion or probability
- g. Assessing the normality of a sample
- 6. Bivariate data
- a. Scatter plots
- b. Types of correlation (e.g., linear, quadratic, and exponential)
- c. Correlation vs. causation
- d. Linear correlation (main focus)
- i. Identifying the direction of the relationship
- ii. Measuring the strength of the relationship
- iii. Using linear regression to make predictions
- iv. Restrictions on using linear regression
- v. Calculating and interpreting residuals
- 7. Sample variability
- a. Sampling distributions for sample means, sample proportions, and sample standard deviations
- i. Using simulation to model sampling variability
- ii. Central limit theorem with applications (normal theory)
- 8. Introduction to statistical inference
- a. Estimation of population parameters using confidence intervals
- b. Conducting hypothesis tests using the probability-value approach
- c. Comparison of simulation-based and normal theory methods, including underlying assumptions
- 9. Inferences involving one population (using simulation-based and normal theory methods)
- a. Creating and interpreting confidence intervals for the population:
- i. Mean
- ii. Proportion
- iii. Standard deviation and variance
- b. Conducting hypothesis tests for the population:
- i. Mean
- ii. Proportion
- iii. Standard deviation and variance
- c. Determining the sample size needed for a given margin of error at a given level of confidence for both means and proportions
- 10. Inferences involving two populations (using simulation-based and normal theory methods)
- a. Independent and dependent samples
- b. Creating and interpreting confidence intervals for:
- i. The difference between two independent means
- ii. The difference between two dependent means
- iii. The difference between two population proportions
- c. Conducting hypothesis tests for:
- i. Two independent means
- ii. Two dependent means
- iii. Two population proportions
- iv. Two population variances or standard deviations
- 11. Additional applications of chi-square
- a. Goodness-of-fit test
- b. Test for independence
- 12. Analysis of variance
- a. Introduction to the analysis of variance technique
- b. The logic behind ANOVA
- c. Applications of single-factor ANOVA