MTH 150

ELEMENTARY STATISTICS

Elementary statistical inference, with an emphasis on ideas, techniques, and applications in the life, physical, and social sciences. Topics include descriptive statistics, confidence intervals, hypothesis testing, contingency tables, multiple regression, and analysis of variance. Not open to mathematics majors or students with credit in MTH 351. Prerequisite: A grade of 2.0 or higher in MTH 094 or meet Department of Mathematics and Computer Science placement criteria through the ALEKS placement test. (Three Credits)


Tentative Course Outline

  • DESCRIPTIVE STATISTICS
    • Central Tendency
      • Mean, median, mode, and their properties
      • Harmonic, geometric, and trimmed mean
    • Variability
      • Range, average deviation, variance, standard deviation, and their properties
      • Interquartile range
      • Relative variability
    • Position
      • Simple ranking, percentile ranking, and z-scores
      • Empirical rule and Chebyshev's Theorem
    • Shape
      • Histograms
      • Stem and leaf displays
      • Box and whisker displays

  • PROBABILITY
    • Counting
      • Multiplicative rule
      • Permutations
      • Combinations
    • Probability Concepts
      • Elementary probability
      • Binomial formula
    • Expected Values
      • Random variables
      • Expected value and variance of a random variable
      • Mean and variance (binomial variable)

  • PROBABILITY DISTRIBUTIONS
    • Binomial Distributions
      • Complete binomial distribution
      • Mean and standard deviation
      • Histogram
    • Poisson Distributions
      • Poisson distribution
      • Poisson approximation to the binomial
    • Normal Distributions
      • Normal Distributions
      • Probabilities and z-scores
      • Means and standard deviations
      • Normal approximation to the binomial

  • THE POPULATION MEAN
    • Confidence Interval of the Mean
      • Distribution of sampling means
      • Central Limit Theorem
      • Confidence interval estimate of the population mean
      • Use of s when σ is unknown
      • Selecting a sample size
    • Hypothesis Test of the Mean
      • Null and alternative hypotheses
      • Critical values and α -risks
      • Drawing conclusions
      • p-values
      • Type II errors and β -risks
    • Differences in Population Means
      • Confidence interval estimates
      • Hypothesis tests
    • Small Samples
      • Student's t-distribution
      • Confidence interval estimates
      • Hypothesis tests
      • Comparing two small population means
    • Comparing More than Two Means
      • Variance between and within shapes
      • F -ratio
      • ANOVA

  • THE POPULATION PROPORTION
    • Confidence Interval of the Proportion
      • Distribution of sample proportions
      • Confidence interval estimate of the population proportion
      • Selecting a sample size
    • Hypothesis Test of the Proportion
      • Type I errors, critical values, p-values
      • Type II errors
      • Operating characteristic and power curves
    • Differences in Population Proportions
      • Confidence interval estimates
      • Hypothesis tests
      • Selecting a sample size

  • CHI-SQUARE ANALYSIS
    • Chi-square Test for Goodness of Fit
      • For uniform distributions
      • For binomial, Poisson, and normal distributions
      • Fits that are too good
    • Chi-square Test for Independence
      • Contingency tables

  • REGRESSION
    • Linear Regression
      • Scatter diagrams
      • Equation of the regression line
      • Interpretation of slope
      • Predictions using regression line
    • Correlation
      • Correlation coefficient
      • Hypothesis test for correlation
Contact R.L. Pryor