CODE: SOR 1213

TITLE: Introduction to Applied Statistics and Data Analysis II

MQF LEVEL: 5

ECTS CREDITS: 4

DEPARTMENT: Junior College

DESCRIPTION:

This is a study unit in statistics is designed to provide students with a background in inferential statistical techniques and data analysis with emphasis on application.  A detailed list of topics is presented below.

Introduction to Confidence Intervals

• Concept of estimation and sampling.
• Difference between population parameters and sample statistics.
• Calculate a confidence interval for population means and proportions.

Hypothesis Testing

• Null hypothesis and alternative hypothesis.
• p-value, significance level (α), Type I and Type II errors.
• One-Sample Hypothesis Test for a Mean using Z-score (known σ) and t-score (unknown σ).
• t-test for two independent samples (pooled and unpooled variances).
• Paired t-test (e.g., before-and-after comparisons).

Chi-Square Tests

• Chi-square goodness-of-fit test.
• Chi-square test for independence.

Correlation

• Concept of correlation and the correlation coefficient.
• Interpretation of correlation values: weak, moderate, and strong correlations.
• Visualizing data using scatter plots.
• Interpreting the strength and direction of relationships.

Linear Regression

• Simple linear regression model
• Understanding the regression line and its interpretation.
• Least squares estimation method for regression coefficients.
• Interpretation of coefficients.

Learning Outcomes

Knowledge and Understanding

By the end of the Study-Unit the student will be able to:

• Describe the concept of a confidence interval and its role in inferential statistics.
• Calculate and interpret confidence intervals for population means (with known and unknown standard deviation) and population proportions.
• Interpret the meaning of the confidence level (e.g., 95% confidence) in the context of the problem.
• Identify when to use the Z-distribution versus the t-distribution in constructing CIs.
• Define and formulate null and alternative hypotheses for various statistical scenarios.
• Describe the concept of the p-value and significance level α.
• Conduct one-sample hypothesis tests for means using both Z-tests and t-tests.
• Perform two-sample hypothesis tests for independent means, including tests for equal and unequal variances.
• Conduct paired sample t-tests for dependent data (before-and-after comparisons).
• Identify and interpret Type I and Type II errors, and understand their impact on hypothesis testing.
• Use p-values to make decisions regarding the null hypothesis and understand the relationship between p-value and significance level.
• Conduct chi-square goodness-of-fit tests to determine how well observed data fit expected distributions.
• Perform chi-square tests for independence using contingency tables to assess relationships between categorical variables.
• Describe the concept of correlation and its role in assessing the strength and direction of relationships between two quantitative variables.
• Calculate and interpret the Pearson correlation coefficient and understand its limitations.
• Construct and interpret scatter plots to visually assess the relationship between two variables.
• Recognize and interpret the strength, direction, and significance of correlation in real-world data.
• Describe the concept of simple linear regression and its application in predicting one variable based on another.
• Perform simple linear regression analysis, estimate the regression coefficients, and make predictions.
• Assess the goodness of fit of a regression model using R-squared and residual analysis.
• Interpret the slope and intercept of a regression model in the context of the data.

Skills

By the end of the Study-Unit the student will be able to:

• Perform inferential statistical analysis using spreadsheets.
• Create and interpret scatter plots and regression lines using spreadsheets.
• Interpret confidence intervals.
• Interpret the p-value in a hypothesis test.
• Apply knowledge of hypothesis testing and regression to real-world data sets to solve practical problems.
• Critically evaluate statistical results and understand the limitations of statistical methods.

Main Reading List

• McClave, J.T. and Sincich, T., 2018. A First Course in Statistics. 12th ed. Boston: Pearson. ISBN 13: 978-1-292-16541-7.
• Triola, M.F., 2021. Elementary Statistics. 14th ed. Hoboken, NJ: Pearson. ISBN-13: 978-0-137-36644-6.
• Sullivan, M., 2020. Statistics: Informed Decisions Using Data. 6th ed. Boston: Pearson. ISBN-13: 978-0-136-87274-0.
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Supplementary Readings

• Agresti, A. and Franklin, C.A., 2017. Statistics: The Art and Science of Learning from Data. 4th ed. Boston: Pearson. ISBN-13: 978-0-133-86082-5.
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STUDY-UNIT TYPE: Lecture

METHOD OF ASSESSMENT: 

Component                                        Weighting

Assignment                                         80%

Classwork                                           20%