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# MAT 157 - Statistics

Last Date of Approval: Fall 2019

4 Credits
Total Lecture Hours: 60
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0

Course Description:
This is a course in basic probability and statistics which includes the study of frequency distributions, measures of central tendency and dispersion, elements of statistical inference, regression, and correlation. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem-solving. This course satisfies a general education requirement in the Math/Science area.

Prerequisites: MAT 035   with C grade or better or the necessary score on the mandatory assessment and placement chart found in the course catalog.

Credit for Prior Learning: There are no Credit for Prior Learning opportunities for this course.

Course Fees: None

Common Course Assessment(s): None

Student Learning Outcomes and Objectives:
Student Learning Outcomes:
Outcome 1:    Analyze data using descriptive statistics.
Outcome 2:    Apply correlation and regression to a data set.
Outcome 3:     Calculate the probability of events.
Outcome 4:    Use software and/or other technologies to analyze large data sets.
Outcome 5:    Analyze data using inferential statistics.

Unit Objectives:
Outcome 1:    Analyze data using descriptive statistics.
Task 1:    Distinguish between applications of descriptive and inferential statistics.
Task 2:    Distinguish between the various types of discrete data (qualitative, ordinal or frequency) and continuous data (metric).
Task 3:    Distinguish between the symbols used for population parameters and sample statistics.
Task 4:    Construct a frequency distribution for a given set of data.
Task 5:    Find the class limits, class boundaries, class marks and class width for a given frequency distribution.
Task 6:    Draw a histogram for a given frequency distribution.
Task 7:    Draw a dot-plot for a given set of data.
Task 8:    Draw a stem-and-leaf diagram for a given set of data.
Task 9:    Identify distribution shapes; identify pertinent features of misleading graphs and correct them.
Task 10:    Construct a box-and-whisker diagram for a given set of data.
Task 11:    Find the mean of a set of ungrouped data.
Task 12:    Find the median of a set of ungrouped data.
Task 13:    Find the mode of a set of ungrouped data.
Task 14:    Compare the mean, median and mode with regard to their advantages and disadvantages as measures of central tendency.
Task 15:    Use subscript and summation notation for the sample mean.
Task 16:    Find the range of a set of ungrouped data.
Task 17:    Find the standard deviation of a set of ungrouped data.
Task 18:    Use summation notation for the sample standard deviation.
Task 19:    Find the z-score for a data value given the mean and standard deviation of the data set.
Task 20:    Find the quartiles for a given set of data.
Task 21:    Calculate the various ranges associated with quartiles, percentiles and deciles.

Outcome 2:    Apply correlation and regression to a data set.
Task 1:    Use the least-squares criterion.
Task 2:    Use total sum of squares, regression sum of squares, and error sum of squares.
Task 3:    Use the coefficient of determination.

Outcome 3:    Calculate the probability of events.
Task 1:    Distinguish between the classical, experiential and subjective methods of probability.
Task 2:    Use the classical method for finding simple probabilities.
Task 3:    Construct and use a sample space for a given probability experiment.
Task 4:    Determine if two events are mutually exclusive.
Task 5:    Find the probability of a compound event using the Addition Rule and Multiplication Rule.
Task 7:    Construct a probability distribution for an experiment given a defined random variable.
Task 8:    Find the mean of a probability distribution.
Task 9:    Find the standard deviation of a probability distribution.
Task 10:    Find the value of binomial coefficients.
Task 11:    Calculate the probability of binomial random variables (Bernoulli trials).
Task 12:    Find the mean of a binomial distribution using the special formula   μ = np.
Task 13:    Find the standard deviation of a binomial distribution using the formula
Task 14:    Use the table of areas under the standard normal curve.
Task 15:    Find z-values corresponding to areas under the standard normal curve.
Task 16:    Determine probabilities for a normally distributed random variable.
Task 17:    Participate in the construction of a sampling distribution given samples from a population.
Task 18:    Experimentally verify the empirical rule theorem.
Task 19:    Determine the mean and standard deviation of a sampling distribution given the mean and standard deviation of the population and the sample size.
Task 20:    Describe the relationship between a population distribution and a sampling distribution that is derived from it.
Task 21:    Find the probability that a sample mean will differ from the population mean by a specified amount when sampling from a distribution.
Task 22:    Construct a normal probability plot and to determine normality.

Outcome 4:    Use software and/or other technologies to analyze large data sets.
Task 1:    Determine the appropriate commands to input and edit data.
Task 2:    State the computer/calculator commands, including any necessary parameters, for drawing histograms.
Task 3:    Use computer/calculator commands to find the mean, median and mode.
Task 4:    Find the standard deviation of a set of data using a computer/calculator.

Outcome 5:    Analyze data using inferential statistics.
Task 1:    Perform the steps that are necessary for finding a confidence interval estimate for a population mean.
Task 2:    Determine a confidence level given α.
Task 3:    Find a point estimate.
Task 4:    Find the sample size that is needed to estimate a population mean to a specified degree of accuracy.
Task 5:    Find a confidence interval estimate for a population mean using student’s t-distribution.
Task 6:    Determine whether to use a z-value or a t-value in a statistical problem.
Task 7:    Formulate hypotheses for a given statistical decision problem.
Task 8:    Choose the proper type of test (one-tail or two-tail) for testing a hypothesis.
Task 9:    Determine the type of error or if a correct decision has been made for a given statistical decision.
Task 10:    State the criteria for a hypothesis test using a large sample.