Santa Barbara City College Course Outline

MATH 117 - Elementary Statistics

MATH 117
Elementary Statistics
Disciplines
Mathematics (Masters Required)
4.000
0 - May not be repeated
General education mathematics course. Introduction to design of experiments, descriptive statistics and sampling distributions. Central Limit Theorem, statistical inference, confidence interval estimation, tests of hypotheses, correlation and linear regression, categorical variables, Chi-square, one-way ANOVA, and multiple comparisons procedure.
64.000-72.000 Total Hours
Total Hours
128.000-144.000 Total Hours
64.000-72.000 Total Hours
Prerequisite: MATH 107 or equivalent based on SBCC's Assessment Center placement via multiple measures.
Prerequisite or Corequisite: None
Concurrent Corequisite: None
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Use statistical terminology accurately.
Produce and interpret statistical software (such as SPSS) outputs with standard statistical computations and analyses, with special attention to large data sets.
Distinguish among different levels of measurement
Use techniques in descriptive statistics including the calculation of measures of central tendency and variation for a given data set and the standard methods of obtaining data.
Recognize and implement an experimental design. Distinguish between an experiment and a longitudinal/observational study.
Distinguish between discrete and continuous random variables and perform computations of mean, variance and standard deviation of a discrete distribution and probabilities of events explained by the normal, the standard normal distribution and the student t-distributions.
Distinguish between the population distribution and the sampling distribution by applying the Central Limit Theorem and recognize and verify assumptions required for the valid application of the Central Limit Theorem.
Use techniques in inferential statistics, with applications to a variety of disciplines including business, social sciences, psychology, life and health sciences, and education
Identify Type I error and Type II error when conducting a test of hypotheses and interpret the level of significance of a test and recognize its relationship to the P-value of a test
Use concepts in correlation and regression in applications.
Analyze the assumed distribution of one categorical variable using the chi square distribution (goodness of fit test) and analyze the association of two categorical variables using the chi square distribution (test of independence of two categorical variables)
Read, analyze and write critiques of statistical studies as reported by the media.
Use statistical software, such as SPSS, to analyze large data sets from a variety of disciplines including business, social sciences, psychology, life and health sciences, and education
Student Learning Outcomes
MATH117 SLO1 - Use statistical core terminology accurately.
MATH117 SLO2 - Identify methods of obtaining data and organize data using numerical and graphical methods.
MATH117 SLO3 - Use measures of central tendency and dispersion to summarize a data set.
MATH117 SLO4 - Calculate probabilities of events explained by the normal and the standard normal distribution and calculate the mean, the variance and the standard deviation of discrete distributions.
MATH117 SLO5 - Carry out a complete test of hypothesis about population parameters, expressing conclusions based on level of significance and on P-values, and estimate population parameters using confidence intervals.
MATH117 SLO6 - Make estimation and inference using Linear Regression and ANOVA analysis.
MATH117 SLO7 - Apply statistical techniques to analyze data from disciplines such as business, social sciences, psychology, and other disciplines.

a.  Introduction to Statistics.  Populations and parameters; samples and statistics.  Sampling and      random numbers.

 

b.  Introduction to sampling and design of experiments.

  1. Standard methods of obtaining data
  2. Advantages and disadvantages of the standard methods of obtaining data
  3. Longitudinal/observational studies v. experiments

c.  Descriptive Statistics

  1. Types of data:  discrete and continuous
  2. Levels of measurement (nominal, ordinal, interval and ratio)
  3. Measures of position:  quartiles, percentiles
  4. Measures of central tendency:  mean, median, and mode
  5. Measures of variability:  range, variance, standard deviation, interquartile range
  6. Calculations of measures of position, central tendency, and variability for a given data set
  7. Frequency distributions:  relative and cumulative frequency tables, histograms.  Constructing frequency tables and histograms for a given data set
  8. Relative measures of position for data from normally distributed populations:  z scores
  9. Calculation and interpretation of z scores for observations from normally distributed populations

d. Sampling Distributions and Probability

  1. Random variables:  discrete vs. continuous
  2. Discrete probability distributions
    1. Mean, variance and standard deviation of discrete random variables
    2. Calculation of mean, variance and standard deviation of discrete distributions
    3. Binomial distribution:  binomial experiments, binomial probability formula; mean, variance and standard deviations of the binomial
  3. Continuous probability distributions
    1. Characteristics of continuous probability distributions, graphs
    2. The general and standard normal distributions; the Student t-distributions
  4. Sampling distributions and the Central Limit Theorem
    1. Sampling Spaces and Probability. The Central Limit Theorem and its required assumptions, including those that allow for reasonable approximations
    2. Comparison between the sampling distribution and the population distribution (the distribution of the individual values of a random variable)
    3. Distribution of the sample mean values for simple random samples when the population standard deviation is known, including the required assumptions.
    4. Distribution of the sample mean values for simple random samples when the population standard deviation is unknown, including the required assumptions
    5. Computation of probabilities associated to ranges of values of the sample mean when the population standard deviation is known or unknown (use of the standard normal distribution and the Student t-distributions)

 

e. Estimation

  1. Point estimates.  Error. Confidence interval estimates
  2. Estimating the population mean with population variance known or unknown
  3. Estimating the population proportion
  4. Estimating differences in two population parameters:  means, proportions
  5. Estimating the mean difference of paired data (dependent samples)
  6. Determination of sample size for achieving a desired maximum margin of error
  7. Applications based on data from a variety of disciplines, including business, social sciences, psychology, life and health sciences, and education

f.  Hypothesis Testing

  1. Null and alternate hypotheses
  2. Type I and Type II errors in tests of hypotheses
  3. Determine and interpret levels of significance and their associated regions of rejection of the null hypothesis when conducting a test.
  4. P-values and their relationship to the level of significance
  5. Tests for means when the population standard deviation is known:  one population, two populations
  6. Tests for means when the population standard deviation is unknown:  one population, two populations, t-tests
  7. Test for the mean difference of paired data (dependent samples)
  8. Tests for proportions:  one population, two populations
  9. Tests for several means:  F-tests (ANOVA)
  10. Applications based on data from a variety of disciplines, including business, social sciences, psychology, life and health sciences, and education

g.  Correlation and Linear Regression

  1. Scatter diagrams
  2. Correlation.  The coefficient of linear correlation. Misuses of correlation. Correlation and causation.
  3. Linear Regression
    1. Line of least squares.  Predicted values using the line of least squares
    2. Misuses of linear regression.  Extrapolation

h.  Categorical Variables

  1. Goodness of fit
  2. Contingency tables
  3. Applications based on data from a variety of disciplines, including business, social sciences, psychology, life and health sciences, and education

i.  One-way Analysis of Variance

  1. F-test for testing the hypotheses of differences among several means
  2. Multiple comparisons procedure
Methods of Instruction
Discussion
Individualized Instruction
Lecture
Mediated Learning
Learning by doing is the focus of this course. Formal lecture is combined with the use of slides, films and projection of computer screens. Assignments in the computer lab and learning center are integral components of the course. Some classes use multimedia CD-ROMs to supplement lectures.
Example A group of n = 20 students take a specialized Module to improve their skill in a task. A pre-module and a post-module test is administered to them. The following results were obtained: Student Pre-module Post-module Difference score score 1 18 22 +4 2 21 25 +4 3 16 17 +1 4 22 24 +2 5 19 16 -3 6 24 29 +5 7 17 20 +3 8 21 23 +2 9 23 19 -4 10 18 20 +2 11 14 15 +1 12 16 15 -1 13 16 18 +2 14 19 26 +7 15 18 18 0 16 20 24 +4 17 12 18 +6 18 22 25 +3 19 15 19 +4 20 17 16 -1 Conduct a test of significance for of the hypothesis that the mean difference in scores is greater than 0, at the 5% level of significance. Construct a 95% confidence interval for this mean difference. Write your conclusions using full sentences.
A. Reading Assignments: will be assigned from the text and from mainstream publications. B. Writing Assignments: submissions of writing samples analyzing and describing conclusions of a statistical test. C. Appropriate Outside Assignments: videotapes in the learning center. D. Use of statistical software (available in the computer lab.) E. Appropriate Assignments that Demonstrate Critical Thinking: students will analyze and critique the methodologies and conclusions of popular media articles or professional journal articles.
The grade for the course will be based on multiple measures of performance in the interpretation and solution of statistical problems. These measures include three one-hour exams and a comprehensive final examination requiring demonstration of problem solving skills. In addition, instructors make use of quizzes, written homework, computer lab assignments and a statistical research project to judge a student's mastery of the subject and familiarity with statistical terminology and procedures.
    Beginning StatisticsWarren, Denley, Alchley, Hawkes Learning Systems, 2014Discovering Statistics and DataJames Hawkes, Hawkes Learning, 2018
  • TI-84 Graphing Calculator
10/07/2018
CAC Approval: 11/05/2018
Board of Trustees: 12/13/2018