MAT 157 - Statistics

1. Discuss statistical processes
   1. Compare and contrast various sampling methods
   2. Distinguish between data types
   3. Discuss the impact of experimental design on experimental results, and
   4. Discuss ethical issues involved in establishing an hypothesis test
2. Generate standard displays of data
   1. Create appropriate tables, charts, and graphs
   2. Calculate representative values of a distribution
   3. Calculate positional values of a distribution, and
   4. Calculate measures of dispersion of a distribution
3. Demonstrate fundamentals of probability
   1. Relate experimental and theoretical probability
   2. Calculate simple probability, and
   3. Calculate the probability of simple, compound, conditional, independent, and mutually exclusive events
4. Analyze probability distributions
   1. Define a probability distribution in terms of a random variable
   2. Calculate the descriptive values of a given probability distribution
   3. Compare and contrast discrete and continuous distributions
   4. Determine the probabilities of events from appropriate distribution tables, and
   5. Apply the normal distribution to binomial events, when appropriate
5. Discuss sampling distributions
   1. State the conditions of the central Limit Theorem
   2. Find the mean and standard error of a sampling distribution, and
   3. Compare and contrast the standard deviation of a sample to the standard error of a sampling distribution
6. Discuss the basics of hypothesis testing
   1. Distinguish between Type I and Type II errors
   2. Discuss the impact of choosing a particular significance level
   3. State the purpose of the hypotheses
   4. State the possible conclusion for an hypothesis test, and
   5. Determine the appropriateness of a one-or two-tailed test
7. Perform significance tests
   1. Write appropriate hypotheses
   2. Execute tests on the mean, proportion, and variance when one population is being studied
   3. Execute tests on the difference of the means and proportions and on the ratio of the variances when two populations are being studied
   4. Perform goodness-of-fit tests
   5. Perform tests on contingency tables, and
   6. Write a clear conclusion for each significance test
8. Construct confidence intervals
   1. Estimate the parameter value.
   2. Calculate the estimate of error, and
   3. Determine the sample size needed to restrict error to a given limit
9. Implement the Analysis of Variance technique
   1. State what is being tested
   2. Write the appropriate hypothesis
   3. Complete an ANOVA table, and
   4. State the conclusion of the test
10. Operate on bivariate data, and
    1. Determine Pearson’s Product Moment, r,
    2. Determine the line of best fit
    3. Test the correlation value r for significance, and
    4. Test the regression coefficients for significance
11. Execute various non-parametric tests