MATH& 146 Introduction to Stats (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 281 - CCN
Prerequisite Completion of GSP
Course Description
Introduction to the analysis of data using descriptive statistics, probability, and inferential statistics. Topics include: data collection methods; measures of center and variation; graphical presentation of data; probability; binomial and normal distributions; confidence intervals; hypothesis tests of one and two parameters, using the normal, Student-t, and chi-square distributions; linear correlation and regression.
Course Content
Descriptive Statistics
A. Statistical vocabulary
B. Sampling methods and designs of statistical studies
C. Summarizing and describing data
D. Central tendency, variation, and distribution
Probability
E. Basic probability
F. Counting methods
G. Discrete probability distributions
H. Continuous probability distributions
Inferential Statistics
I. Confidence intervals
J. Hypothesis testing using the normal, student-t, and Chi-square distribution
K. Linear correlation and regression
Student Outcomes
Descriptive Statistics:
1. Identify and describe various probabilistic sampling methods.
2. Identify components of experimental and observational studies.
3. Identify uses and misuses of statistics.
4. Construct appropriate representations of data, such as tables (contingency tables and frequency distributions), and graphs (histograms, scatterplots, and boxplots.)
5. Calculate measures of center (mean, median) with and without technology.
6. Calculate measures of variation (range, standard deviation, variance) with and without technology.
Probability:
7. Calculate probability for simple and compound events using both empirical data and sample spaces.
8. Use appropriate counting methods (fundamental counting rule, permutations, combinations).
9. Solve problems using discrete probability distributions, including binomial distributions.
10. Determine the mean and standard deviation of discrete probability distributions.
11. Solve problems using continuous distributions, including normal and Student t distributions.
12. Apply the Central Limit Theorem to calculate the mean and standard deviation of sampling distributions.
Inferential Statistics:
13. Determine appropriate sizes of samples.
14. Generate confidence intervals for means and proportions.
15. Select and perform hypothesis tests for the mean of one population, proportion of one population, means of two populations, and proportions of two populations.
16. Use the chi-square distribution to perform a hypothesis test such as goodness-of-fit or test of independence.
17. Analyze two-variable data using scatter plots, linear correlation coefficients, and linear regression lines, using technology to calculate these items.
18. Determine whether there is a statistically significant linear correlation between two variables.
Communication and General Skills:
19. Communicate the results of data analysis clearly and precisely in both technical and non-technical words, including the use of the following: correct statistical vocabulary; graphical, symbolic, and numeric support for conclusions; indications of the strength and limitations of conclusions.
20. Engage in experiential learning of key concepts through classroom activities and/or projects.
21. Draw logical conclusions related to a specific problem by integrating the use of the following: sampling; summary statistics and presentation of data; and either confidence intervals, hypothesis tests or regression analysis as appropriate.
Degree Outcomes
Quantitative & Symbolic Reasoning: Graduates utilize mathematical, symbolic, logical, graphical, geometric, or statistical analysis for the interpretation and solution of problems in the natural world and human society.
Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.
Effective Communication: Graduates will be able to exchange messages in a variety of contexts using multiple methods.
Information Competency: Graduates will be able to seek, find, evaluate and use information, and employ information technology to engage in lifelong learning.
Intercultural Engagement: Graduates demonstrate self-efficacy in intercultural engagement to advance equity, diversity, and inclusion through reflections and expressions of cultural humility, empathy, and social and civic engagement and action. Further, graduates examine how identities/positionalities such as races, social classes, genders, sexual orientations, disabilities, and cultures impact perceptions, actions, and the distribution of power and privilege in communities, systems, and institutions.
Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50
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