MAT 157 - 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 6:    Find conditional probabilities.
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.
Task 11:    Test a hypothesis about a population mean.