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MAT129 - Statistics
Catalog Description: Studies descriptive data with graphical and numerical techniques, binomial and normal probability distributions, estimation and sampling, hypothesis testing, and linear regression models. Emphasis is on practical applications, including using MINITAB software. Prerequisite: MAT 092 or higher or by placement
Lecture: 3 hrs.
Course Learning Outcomes (CLOs):
Upon successful completion of this course, the student will be able to:
1. Given a set of measurements, generate a graphical display (such as a frequency distribution or histogram)
2. Given a set of measurements, compute the basic measures of central tendency (mean, median, mode) and dispersal (range, variance, standard deviation).
3. Given the graph of a distribution of measurements, or a description of such a graph, apply Empirical Rule or Chebyshev's Theorem to describe the distribution of data and identify the existence of any outliers.
4. Compute simple theoretical and empirical probabilities, applying the Addition, Multiplication, and Complement Rules as needed.
5. Given a discrete random variable x, generate a probability distribution (empirically or theoretically) and/or verify that the distribution is valid.
6. Given a valid discrete probability distribution, find simple probabilities and compute the mean and standard deviation of the random variable associated with the distribution.
7. Given a table of probabilities for the standard normal curve, find probabilities for any given normal distribution or, given the area of any segment under the normal curve, find the associated z - value or x - value.
8. Given a randomly distributed population, use the Central Limit Theorem to describe any corresponding sampling distribution and find probabilities associated with the sample mean.
9. Given appropriate sample data, formulate a confidence interval for the mean or binomial proportion.
10. Given an appropriate test scenario and sample data, conduct a test of hypothesis for the mean or binomial proportion.
11. Given any set of paired sample data, find the line of best fit and correlation coefficient.*
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
I. Introduction and Descriptive Statistics
A. Organizing Data
1. Grouping data
2. Graphs and charts
3. Stem-and-leaf diagrams
B. Descriptive Measures
1. Measures of central tendency
2. Measures of dispersion
b. Standard deviation
c. Empirical Rule
3. Measures of position
C. Populations vs. Samples
II. Probability Concepts
A. Classical Probability
1. Sample space and events
2. Laws of probability
B. Discrete Random Variables
1. Probability distributions
2. Mean and standard deviation
3. Binomial probability distribution
C. Normal Distribution
1. Normal curves
2. Normally distributed populations
3. Normal approximation to the binomial distribution
A. Random samples
B. Central limit theorem
C. Sampling distribution of the mean
IV. Inferential Statistics
A. Confidence intervals for the mean
1. Large sample confidence intervals for the mean
2. Sample size considerations
3. Confidence intervals for a normal population mean
B. Hypothesis tests for the mean
1. Nature of hypothesis testing
2. Large sample hypothesis tests for a population mean
C. Inference for two means or proportions (optional, time permitting)
1. Large sample inference for two population means
2. Two normal populations with equal standard deviations
V. Bivariate Data
1. Linear regression
2. Linear correlation
Effective Term: Fall 2016