Math 113: Study Guide - Final Exam

  1. Identify the distribution illustrated. Six parts. Be sure you know the uniform, binomial, normal, student's t, chi-square, and f distributions.
  2. Draw and label vertical lines to identify the mean, median, and mode of the distribution.
  3. Find the mean, standard deviation of a binomial experiment with n and p given. Then, find the probability of a certain number of successes (use the Binomial program on the calculator).
  4. Find the critical values for the normal and Student's T distributions. Remember that the critical value notation is always for a right tail test.
  5. Given a set of data, find the mean, standard deviation, median, range, and find a percentile.
  6. Given a probability distribution, find the mean, variance, and standard deviation. Use the pdist program on the calculator.
  7. Find the probability of a randomly selected individual having a given score and the probability of a mean of a sample having a given score.
  8. Find the expected value of a game. A simple game is described, determine the payoffs and then compute the expected value (recall the expected value is the same as the mean of a probability distribution).
  9. Write the null and alternative hypotheses for the given claims. Three parts.
  10. Definitions - matching. Not all definitions are used, but know the definitions of the following: Alternative Hypothesis, Binomial Experiment, Class Mark, Class Boundary, Conclusion, Confidence Interval, Confidence Limit, Correlation Coefficient, Critical Value, Decision, Degrees of Freedom, Hypothesis, Median, Midrange, Null Hypothesis, Parameter, Probability Distribution, Sample Size, Statistic, Test Statistic, Type I Error, Type II Error.
  11. Explain why the deviations from the mean must be squared when finding the variation. Draw a figure to illustrate. This is from the notes on the derivation of variation, variance, and standard deviation.
  12. Shade the region and find the area under the standard normal curve. Four parts.
  13. Given a p-value and an original claim, state the conclusion. Fill in the blank.
  14. Given a confidence interval, find the sample mean and perform a two-tailed hypothesis test.
  15. One-way analysis of variance problem. Write the null and alternative hypotheses. The summary statistics are given, enter those into the calculator to complete the ANOVA table. Find the critical value and give the conclusion.
  16. Simple probability problem. Items are in a hat / bag and an item is randomly selected. Find some probabilities.
  17. Correlation and Regression. A scatter plot is given along with the values of n, r, y bar, and the regression equation. Describe the linear correlation (use table A6) - ie, write a conclusion (there is no significant linear correlation, there is significant positive linear correlation, or there is significant negative linear correlation). Write the regression model (be sure to use the right equation). Estimate y for a given value of x.
  18. Two-way analysis of variance problem. Information describing the sampling is given as well as the Sum of Squares (variation) values. Complete the rest of the table. Give a simple yes / no answer for each of the hypothesis tests.


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