MATH 1774: Statistics

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Subject
Mathematics
Credit Hours 4.0 Lecture Hours 4.0 Lab Hours 0.0
Type of Credit
Baccalaureate/Transfer
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Course Description
This course focuses on statistical reasoning and on solving problems using real-world data rather than on computational skills. Use of technology-based computations (such as graphing calculators with a statistical package, spreadsheets, or statistical computing software) is required with emphasis on interpretation and evaluation of statistical results. Topics include data collection processes (observational studies, experimental design, sampling techniques, bias), descriptive methods using quantitative and qualitative data, bivariate data, correlation, and least-squares regression, basic probability theory, probability distributions (normal distributions and normal curve, binomial distribution), chi-square tests, one-way analysis of variance, confidence intervals and hypothesis tests using p-values. Students cannot receive credit for both MATH 1774 and BSNS 2514. IAI: M1 902 Mathematics. IAI: BUS 901 Business.
Prerequisite(s)
MATH 1424 or MATH 0985 with a grade of C or better, appropriate assessment score, or High School Transitional Math: quantitative literacy (QL) or STEM pathway - Must be completed prior to taking this course.

At the end of this course, students will be able to:

  • Organize data using frequency distributions and graphs
  • Distinguish between the different types of studies and different types of random sampling
  • Describe (summarize) data using measures of central tendency and dispersion
  • Perform calculations associated with fundamental distributions and solve related application problems
  • Construct confidence intervals for means and proportions
  • Perform hypothesis tests for means and proportions using p-values.
  • Calculate correlation coefficient and check its significance
  • Estimate a regression equation and interpret its coefficients
  • Use technology to complete basic statistical analyses
Topical Outline

A.    Data Collection

        1.    Introduction to the Practice of Statistics

        2.    Observational Studies vs Designed Experiments

        3.    Simple Random Sampling

        4.    Other Effective Sampling Methods

        5.    Bias in Sampling

        6.    The Design of Experiments

B.    Descriptive Statistics

        1.    Organizing Qualitative Data

        2.    Organizing Quantitative Data: The Popular Displays

        3.    Additional Displays of Quantitative Data

        4.    Graphical Misrepresentations of Data

C.    Numerically Summarizing Data

        1.    Measures of Central Tendency

        2.    Measures of Dispersion

        3.    Measures of Central Tendency and Dispersion from Grouped Data

        4.    Measures of Position and Outliers

        5.    The Five-Number Summary and Boxplots

D.    Describing the Relation Between Two Variables

        1.    Scatter Diagrams and Correlation

        2.    Least Squares Regression

        3.    Diagnostics on the Least-Square Regression

        4.    Contingency Tables and Association

E.    Probability and Probability Distributions

        1.    Probability Rules

        2.    The Addition Rule and Complements

F.    Discrete Probability Distributions

        1.    Discrete Random Variables

        2.    The Binomial Distribution

G.   The Normal Probability Distribution

        1.    Properties of the Normal Distribution

        2.    Applications of the Normal Distribution

        3.    Assessing Normality

H.    Sampling Distributions

        1.    Distribution of the Sample Mean

        2.    Distribution of the Sample Proportion

I.     Estimating the Value of a Parameter

        1.    Estimation a Population Proportion

        2.    Estimating a Population Mean

        3.    Estimating a Population Standard Deviation

        4.    Putting It Together: Which Procedure Do I Use?

J.     Hypothesis Tests Regarding a Parameter

        1.    The Language of Hypothesis Testing

        2.    Hypothesis Tests for a Population Proportion

        3.    Hypothesis Tests for a Population Mean

        4.    Hypothesis Tests for a Population Standard Deviation

K.    Inferences on Two Samples

        1.    Inference about Two Population Proportions

        2.    Inference about Two Means: Dependent Samples

        3.    Inference about Two Means: Independent Samples

L.     Inference on Categorical Data

        1.    Goodness-of-Fit Test

        2.    Tests for Independence and the homogeneity of Proportions

M.  Comparing Three or More Means

        1.    One-Way Analysis of Variance