# Statistics II

## Course Description

Investigates confidence interval estimation; tests of significance including z-tests, t-tests, ANOVA, and chi-square; and inference for linear regression. Applications are investigated from science, business, and social science perspectives. Graphing calculator with advanced statistical programs required and/or computer software. Prerequisites: MTH 243 and its prerequisite requirements. Audit available.

## Intended Outcomes

Upon successful completion of this course, students will be able to:

1. Statistically analyze observational and experimental studies and critically assess results from the same.
2. Clearly communicate statistical procedures and results.
3. Read with understanding scholarly publications and critically assess public dissemination of statistical information.
4. Adapt statistical techniques and reasoning to other disciplines and vocations.

## Alignment with Institutional Core Learning Outcomes

 indepth 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication) indepth 2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving) indepth 3. Apply the knowledge, skills and abilities to enter and succeed in a defined profession or advanced academic program. (Professional Competence) 4. Appreciate cultural diversity and constructively address issues that arise out of cultural differences in the workplace and community. (Cultural Awareness) min 5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

## Outcome Assessment Strategies

Assessment shall include some combination of the following:

• Class participation
• Group projects
• Presentations
• Portfolios
• Research papers
• Homework assignments
• Written paper
• Quizzes
• Exams
• Other assessments of the instructors choosing

## Course Activities and Design

Concepts will be introduced using lecture, group activities, calculator and/or computer programs, and computer laboratory explorations. Students will communicate their results orally and in writing.

## Course Content (Themes, Concepts, Issues and Skills)

1.0 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
The instructional goal is to explore and analyze various random variables and probability distributions.

1.1 Explore probability distributions:

1.1.1 Normal.
1.1.2 Student’s t.
1.1.3 F.
1.1.4 Chi-square.

2.0 ESTIMATION: ONE SAMPLE
The instructional goal is to estimate a population parameter by calculating a confidence interval.

2.1 Identify and describe terminology:

2.1.1 Confidence coefficient.
2.1.2 Confidence level.
2.1.3 Confidence interval.

2.2 Check the conditions associated with a confidence interval for a population mean.
2.3 Check the conditions associated with a confidence interval for a population proportion.
2.4 Calculate and interpret a confidence interval for a population mean.
2.5 Calculate and interpret a confidence interval for a population proportion.
2.6 Calculate a sample size to attain a desired margin of error and confidence level.
2.7 Using technology, input a sample and execute the commands to create a confidence interval; interpret the output.

3.0 STATISTICAL INFERENCE: ONE SAMPLE
The goal is to utilize sample information to test whether a population parameter is less than, not equal to, or greater than a specified value.

3.1 Perform a two-sided test using:

3.1.1 A test of significance.
3.1.2 A confidence interval.

3.2 Calculate sample size.
3.3 Identify and describe terminology:

3.3.1 Null and alternative hypotheses.
3.3.2 Test statistic.
3.3.3 Distinguish between significance and hypothesis testing
3.3.4 Type I and Type II errors,  and .
3.3.5 Observed significance level: P-value.

3.4 Check the conditions associated with a test of significance about a population mean.
3.5 Check the conditions associated with a test of significance about a population proportion.
3.6 Construct and interpret a z-test about a population mean.
3.7 Construct and interpret a t-test about a population mean.
3.8 Construct and interpret a z-test about a population proportion.
3.9 Using technology, input a sample and execute the commands to perform a t-test or a z-test; interpret the output.
3.10 Calculate and interpret the power of a z-test.

4.0 ESTIMATION AND STATISTICAL INFERENCE: TWO SAMPLES
The instructional goal is to utilize sample information to infer whether a difference exists between two population means or two population proportions.

4.1 Perform a two-sided test using:

4.1.1 A test of significance.
4.1.2 A confidence interval.

4.2 Check the conditions associated with a confidence interval or test of significance about the difference between two population means using two independent samples.
4.3 Check the conditions associated with a confidence interval or test of significance about the difference between two population proportions using two independent samples.
4.4 Check the conditions associated with a confidence interval or test of significance about the mean difference between two populations using paired samples.
4.5 Construct and interpret a confidence interval about the difference between two population means using two independent samples.
4.6 Construct and interpret a t-test about the difference between two population means using two independent samples.
4.7 Construct and interpret a confidence interval about the difference between two population proportions using two independent samples.
4.8 Construct and interpret a z-test about the difference between two population proportions using two independent samples.
4.9 Construct and interpret a confidence interval about the mean difference between two populations using paired samples.
4.10 Construct and interpret a t-test about the mean difference between two populations using paired samples.
4.11 Using technology, input two independent samples and execute the commands to perform a two-sample difference of means confidence interval; interpret the output.
4.12 Using technology, input two independent samples and execute the commands to perform a two-sample difference of means test; interpret the output.
4.13 Using technology, input two independent samples and execute the commands to perform a two-sample difference of proportions confidence interval; interpret the output.
4.14 Using technology, input two independent samples and execute the commands to perform a two-sample difference of proportions test; interpret the output.
4.15 Using technology, input two paired samples and execute the commands to perform a one-sample confidence interval; interpret the output.
4.16 Using technology, input two paired samples and execute the commands to perform a one-sample t-test; interpret the output.

5.0 ANALYSIS OF VARIANCE (ANOVA)
The instructional goal is to design and analyze a sampling experiment to compare the means of more than two populations.

5.1 Identify and describe terminology:

5.1.1 Response (dependent) variable.
5.1.2 Factor (independent variable, stimulus).
5.1.3 Levels (treatments) of a factor.
5.1.4 Sum of squares for treatments (SST) and error (SSE).
5.1.5 Mean square for treatments (MST) and error (MSE).

5.2 Check the conditions associated with an ANOVA test.
5.3 Compare the treatment means.
5.4 Summarize the results of the F test in an ANOVA table.
5.5 Using technology, input sample data and execute the commands to perform ANOVA; interpret the output.
5.6 Use a multiple comparisons method to determine which pairs of means differ; interpret the results.

6.0 CHI-SQUARE TESTS AND CONTINGENCY TABLES
The instructional goal is to explore a non-parametric procedure on categorical variables.

6.1 Identify and describe terminology:

6.1.1 Multinomial probabilities.
6.1.2 Contingency table.
6.1.3 Marginal probabilities.

6.2 Check the conditions associated with a goodness-of-fit test.
6.3 Check the conditions associated with a test of independence.
6.4 Check the conditions associated with a test of homogeneity.
6.5 Perform a goodness-of-fit test about the probability distribution of a random variable.
6.6 Determine whether two classifications of nominal data are independent using a contingency table, multinomial probabilities, and a chi-square test.
6.7 Using technology, input sample data, choose commands to perform an appropriate chi-square test; interpret the output.

7.0 SIMPLE LINEAR REGRESSION AND CORRELATION
The instructional goal is to explore a straight-line relationship between two random variables, and use the least-squares line as a basis for inference about a population from which our observations are a sample.

7.1 Identify the explanatory variable and the response variable.
7.2 Check the conditions associated with constructing a least-squares linear regression model.
7.3 Construct a scatterplot of the sample data.
7.4 Identify the least-squares estimates of the intercept and the slope (the parameters) of the population regression model.
7.5 Specify the probability distribution of the random error term, and estimate the standard deviation of this distribution.
7.6 Evaluate the utility of the model:

7.6.1 Conduct a test of significance to determine whether the data provide sufficient evidence to indicate that the explanatory variable contributes information for the linear prediction of the response variable.
7.6.2 Construct and interpret a confidence interval to estimate the slope of the population regression model.
7.6.3 Calculate and interpret the sample correlation coefficient .
7.6.4 Calculate and interpret the coefficient of determination .

7.7 Use the least-squares line for estimation and prediction:

7.7.1 Construct and interpret a confidence interval for the mean value of the response value when the explanatory variable takes on a specific value.
7.7.2 Construct and interpret a prediction interval for an individual value of the response value when the explanatory variable takes on a specific value.

7.8 Using technology, input sample data and execute the commands to produce a least-squares regression equation, a fitted line, a residual plot, and ; interpret the output.

## Department Notes

This is the second term of a two-term sequence (MTH 243 and MTH 244). This course is intended to provide an introduction to statistics in a data-based setting.