MTH4445 ENGINEERING PROBABILITY AND STATISTICS I
3 Credit Hours
Student Level:
This course is open to students on the college level in either the Freshman or Sophomore year.
Catalog Description:
MTH4445 - Engineering Probability and Statistics I (3 Hrs.)
Graphical and numerical methods for summarizing and describing datasets. Probability, introduction to discrete and random variables, inferential studies about population parameters.
Course Classification:
Lecture
Prerequisites:
A minimum grade of C in MTH 4440- Calculus II
Controlling Purpose:
To equip science and pre-engineering students with a knowledge of graphical and numerical methods of analyzing statistics data. The course requires the student to furnish his or her TI-83 or TI 84 graphing calculator.
Learner Outcomes:
Upon completion of the course, the student will:
- Use graphical and numerical methods to summarize and describe data.
- Demonstrate a basic understanding of probability and statistics. Describe and use different discrete and continuous random variables.
- Identify bivariate probability distributions, covariance and correlation and the probability distribution of a statistic.
- Perform estimation and hypothesis testing of population parameters
Unit Outcomes for Criterion Based Evaluation:
The following outline defines the minimum core content not including the final examination period. Instructors may add other material as time allows.
UNIT 1: Descriptive Statistics
Outcomes: Upon completing this unit, the student will be able to use graphical methods to explore, summarize and describe data
- Identify statistical concepts and definitions
- classify data as categorical or quantitative
- Display and interpret categorical and quantitative data using graphical tools
- Calculate measures of central tendency, variation, and relative standing
UNIT 2: Probability
Outcomes: Upon completing this unit the student will be able to demonstrate an understanding of basic probability concepts
- Determine outcomes, events, and sample space of a given experiment
- Calculate probability of a simple event
- Determine compound and complimentary events and calculate their probabilities
- Use additive and multiplicative rules to compute probabilities
- Formulate and compute conditional probability
- Identify mutually exclusive and independent events and compute their probabilities
- Apply Bayes Rule
- Apply counting rules (multiplicative, permutations, partition and combinations) to count number of experimental outcomes
UNIT 3: Discrete Random Variables
Outcomes: Upon completing this unit, the student will be able to describe and use different discrete random variables.
- Define a random variable
- Describe a discrete random variable and its probability distribution
- Calculate the Expected Value and standard deviation of a random variable
- Identify and use Bernoulli, Binomial, Geometric, Negative Binomial and poison random variables (experiment, probability distribution, mean and variance)
UNIT 4: Continous Random Variables
Outcomes: Upon completing this unit, the student will be able to describe and use different continuous random variables
- Describe a continuous random variable and its probability density function
- Calculate the expected value and standard deviation of a continuous random variable
- Describe uniform, normal and Gamma-type random variables and their properties
- Apply normal approximation to binomial distributions
- Apply descriptive methods for assessing normality
- Calculate the probability of events of a continuous random variable
UNIT 5: Sampling Distributions
Outcomes: Upon completing this unit the student will be able to Identify bivariate probability distributions, covariance and correlation of a statistic (sampling distribution)
- Identify Bivariate probability distribution
- Calculate and interpret covariance and correlation or two random variables
- Describe the sampling distribution of the sample mean
- Describe and apply sampling distributions (Chi-square, T, and F) related to normal distribution and the corresponding probability tables
- Use sampling distributions to calculate the probability of events involving sample statistics and population parameters
UNIT 6: Estimation Using Confidence Intervals
Outcomes: Upon completing this unit, the student will be able to find estimates of population means, proportions, and variances and develop procedures for finding point estimate, confidence interval, and required sample size.
- Describe point and interval estimators
- Construct confidence intervals for population mean with known/ unknown variance.
UNIT 7: Hypothesis Testing
Outcomes: Upon completing this unit, the student will be able to perform hypothesis testing of population parameters.
- Identify hypothesis testing concepts including null and alternative hypothesis, test statistic, rejection region, and type I and type II errors
- Contrast one tailed vs. two tailed statistical tests.
- Test population mean for large and small samples
- Describe and calculate the observed significance level (p-value)
- Test the difference between population means: independent large (small) samples with identical (different) population variances and matched pairs
- Test population proportion and difference between population proportions: independent large samples
- Test the population variance and the ratio of two population variances
Projects Required:
None.
Textbook:
Statistics for engineering and the sciences, William Mendenhall and Terry Sincich, 6th edition, CRC Press/Taylor& Francis, 2016. Please Contact Bookstore for current textbook.
Materials/Equipment Required:
Graphing calculator (TI-83 or TI-84 series calculator)
Attendance Policy:
Students should adhere to the attendance policy outlined by the instructor in the course syllabus.
Grading Policy:
The grading policy will be outlined by the instructor in the course syllabus.
Maximum class size:
Based on classroom occupancy
Course Time Frame:
The U.S. Department of Education, Higher Learning Commission and the Kansas Board of Regents define credit hour and have specific regulations that the college must follow when developing, teaching and assessing the educational aspects of the college. A credit hour is an amount of work represented in intended learning outcomes and verified by evidence of student achievement that is an institutionally-established equivalency that reasonably approximates not less than one hour of classroom or direct faculty instruction and a minimum of two hours of out-of-class student work for approximately fifteen weeks for one semester hour of credit or an equivalent amount of work over a different amount of time. The number of semester hours of credit allowed for each distance education or blended hybrid courses shall be assigned by the college based on the amount of time needed to achieve the same course outcomes in a purely face-to-face format.
Refer to the following policies:
402.00 Academic Code of Conduct
263.00 Student Appeal of Course Grades
403.00 Student Code of Conduct
Disability Services Program:
Cowley College, in recognition of state and federal laws, will accommodate a student with a documented disability. If a student has a disability which may impact work in this class and which requires accommodations, contact the Disability Services Coordinator.
DISCLAIMER: THIS INFORMATION IS SUBJECT TO CHANGE. FOR THE OFFICIAL COURSE PROCEDURE CONTACT ACADEMIC AFFAIRS.
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