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# MAT 158 - Statistics II

Course Department: Mathematics
Last Date of Approval: Fall 2019

3 Credits
Total Lecture Hours: 45
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0

Course Description:
This is the second course in the statistics sequence. It includes the study of additional topics in correlation, regression, and statistical inference. The course also includes the topics of chi-square procedures, analysis of variance, non-parametric methods, and statistical quality control. 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 157 - Statistics  or equivalent.
Mode(s) of Instruction: traditional/face-to-face, and/or online

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:     Construct confidence intervals.
Outcome 2:     Evaluate hypothesis tests.
Outcome 3:    Apply chi-squared procedures.
Outcome 4:     Apply analysis of variance.
Outcome 5:    Apply inferential methods in regression and correlation.

Unit Objectives:
Outcome 1:    Construct confidence intervals.
Task 1:    Construct a normal probability plot with the aid of Table III.
Task 2:    Identify distribution shapes from normal probability plots.
Task 3:    Detect outliers from normal probability plots.
Task 4:    Construct and interpret confidence intervals for the means of two normal populations using independent samples when the population standard deviations are unknown but assumed equal.
Task 5:    Construct and interpret confidence intervals for the means of two normal populations using independent samples when the population standard deviations are unknown and assumed unequal.
Task 6:    Construct and interpret confidence intervals to compare the means of two populations using paired samples when the population of paired differences is normally distributed.
Task 8:    Construct and interpret confidence intervals for one population proportions.
Task 9:    Calculate the margin of error in estimating a population proportion by a sample proportion.
Task 10:    Compute the sample size required to meet the specifications of the margin of error and confidence level of a confidence interval for population proportion.
Task 11:    Construct and interpret confidence intervals for the difference between two population proportions using independent samples.
Task 12:    Calculate the margin of error in estimating the difference between two population proportions.
Task 13:    Compute the sample size required to meet the specifications of the margin of error and confidence level of a confidence interval for the difference in population proportions.

Outcome 2:    Evaluate hypothesis tests.
Task 1:    Define and apply the concepts of Type I and Type II errors.
Task 2:    Compute Type II error probabilities.
Task 3:    Calculate the power of a hypothesis test.
Task 4:    Draw a power curve.
Task 5:    Determine the p-value of a hypothesis test.
Task 6:    State and apply the steps for performing a hypothesis test using the p-value approach to hypothesis testing.
Task 7:    Perform a hypothesis test for a population mean when the population being sampled has a symmetric distribution.
Task 8:    Perform a hypothesis test for the means of two normal populations using independent samples when the population standard deviations are unknown but assumed equal.
Task 9:    Perform a hypothesis test for the means of two normal populations using independent samples when the population standard deviations are assumed unequal.
Task 10:    Perform a hypothesis test to compare the means of two populations using independent samples when the populations have the same shape.
Task 11:    Perform a hypothesis test to compare the means of two populations using paired samples when the population of paired differences is normally distributed.
Task 12:    Perform a hypothesis test to compare the means of two populations using paired samples when the population of paired differences has a symmetric distribution.
Task 13:    Determine which procedure to use to compare the means of two populations.
Task 14:    Perform hypothesis tests for one population proportions.
Task 15:    Perform hypothesis tests for two population proportions using independent samples.

Outcome 3:    Apply chi-squared procedures.
Task 1:    Perform the chi-square goodness-of-fit test.
Task 2:    Determine chi-square values from the table.
Task 3:    Perform the chi-square independence test.
Task 4:    Perform the chi-square test for population standard deviation.
Task 5:    Construct and interpret a confidence interval for population standard deviation

Outcome 4:    Apply analysis of variance.
Task 1:    Determine F-values from the table.
Task 2:    Perform the one-way analysis of variance test.
Task 3:    Perform the Tukey multiple-comparison method.
Task 4:    Perform the Kruskal-Wallis test.

Outcome 5:    Apply inferential methods in regression and correlation.
Task 1:    Explain what it means for a set of data to satisfy the assumptions for the regression model.
Task 2:    Calculate the standard error estimate.
Task 3:    Calculate an estimate for the mean of the population of y-values that correspond to a particular x-value.
Task 4:    Perform a residual analysis.
Task 5:    Perform prediction for an individual y-value corresponding to a particular x-value.
Task 6:    Perform inferences for the slope of the population regression line.
Task 7:    Perform inferences in correlation.

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