2. Histogram
- Frequency and relative frequency distributions and histograms. (Students will NOT be required to draw histograms by hand on any test or examination)
- HISTogram, HIST with the subcommands STARt and INCRement Using the Minitab output in the workbook to read and interpret the histogram output. Class, class boundaries, class frequencies, and shape. Effect of the number of classes used in a histogram on the shape of the histogram
- Histogram for discrete and categorical data
- Typical sample shapes
3. Stem and Leaf Plot
- Plot by hand. Three kinds of plots: 1, 2, and 5 leaf categories per stem.
- truncation, stem unit, leaf unit
- stem unit = 10 x leaf unit
- increment = stem unit/[# leaf categories per stem]
- Stem and leaf plot on Minitab. "Depths".
4. Dotplot(on Minitab only). Reading approximate sample values on the dotplot scale
Data Analysis
5. Measures of Location
- sample mean (x-bar), sample median (m)
- mean is sensitive to outliers, median is not (outliers are extreme sample values which are either infrequently occurring members of the population, or which do not belong to the sample at all, such as measurement errors, recording errors, measurements from the wrong population etc.)
- x-bar, median symmetry and skewness
- x-bar and median on Minitab: MEAN, MEDIan, DESCribe
6. Measures of Variation
Total variation (SSTo), sample variance (s2) and sample standard deviation (s)(computational formula) Minitab: STDEV, DESCribe, use of LET to obtain s2
7. Change of Units of Measurement
8. Measures of Relative Position
- Empirical rule and z-scores
- Percentiles, quartiles and their interpretation
- Special Percentiles (quartiles)
9. Boxplots
- Construction by hand
- The boxplot on Minitab.
- Using the boxplot to give a detailed description of shape
- Use of STEM with the subcommand TRIM
10. Probability
- Notions of probability
- Solving problems which require setting up the sample space (using a tree or otherwise), describing certain events, and using the equally likely approach to calculate the probability of their occurrence
- Operations on events and the associated rules of probability.
- Probability
- Probability calculations from a contingency table
- Conditional probability, the multiplication rule, and independence
- Let's Make a Deal Game
- Bayes Rule
11. Population and Random Variables
- Discrete random variable, its probability table (i.e. its probability mass function), and its probability histogram; calculating probabilities from the probability table
- Mean x-bar, variance s2 and standard deviation
- Probability distribution of a random variable as a "theoretical model" for the distribution of measurements of a population.
12. Binomial Distribution
- Meaning of n! and the combinatorial formula.
- Definition of a binomial experiment, the binomial random variable and examples
- Probability distribution of "X = the total number of heads", when an unfair coin is tossed three times and the binomial formula for P(X= x)
- Relationship between the shape of the binomial distribution and the probability of success 'p'
- Mean, variance and standard deviation ]
- Use of the formula, and, pmf and cdf tables to calculate binomial probabilities and word problems
- Calculating binomial probabilities on Minitab
13. Normal Distribution
- Continuous random variables
- Normal distributions, mean variance and standard deviation
- Standard normal distribution and use of the standard normal table
- Word problems, derivation of the empirical rule
- Standard Normal percentiles [WB p. 108]
- Z Scores & the Normal Distribution
- Percentiles of a general Normal distribution, word problems
- Changing the Units of measurement for a Normal Distribution
- Normal Approximation to the Binomial, word problems
- Normal Approximation to Binomial
14. Properties of the Sample Mean (the Central Limit Theorem)
- Properties of the sample mean and the Central Limit Theorem
- Applications of the CLT: word problems
- Central Limit Theorem
15. One sample inference
- Margin of error E, reliability (level of confidence), and confidence interval (Z-interval) for the known variance case.. T-interval (note: we will not use the Z-interval in practice but only as a means of developing the T-interval when the variance is unknown)
- The T Distribution
- Constructing a T-confidence interval by hand and using Minitab. Interpreting a confidence interval
- Confidence Intervals
- Affect of sample size and level of confidence on the margin of error
- Selecting the necessary sample size to obtain a CI with margin of error E and level of confidence 100(1 - alpha)%
- Testing Hypothesis
- T-test
16. Confidence Interval for the Population Proportion p
- Basic properties of the estimate of a population proportion "p"
- Small sample "exact" confidence interval
- Large sample approximate confidence interval for "p"
- Selecting the necessary sample size to obtain a CI with margin of error E and level of confidence 100(1 - alpha)% with and without a prior estimate for "p"
17. Two sample inference
18. Correlation and the Least Squares Line
- The idea of bivariate data
- Equation of a straight line, slope, intercept
- Notion of association (correlation)
- Regression
- Spearman's rank correlation
- Drawing a scatterplot by hand to develop Pearson's sample correlation coefficient r
- Interpretation of r
- Correlation and causality
- Least squares line and the use of coefficient of determination as a measure of fit
- Scatterplots, correlation and the least squares line on Minitab [WB p.62-63]
- Bivariate Data
- Guessing Correlation
- Least Square Line
- Putting Points
Box Models
Chi-square Tests