Math 113 Study Guide - Final Exam

1. Match the distribution with its graph. The Uniform, Binomial, Normal, Student's t, Chi-square, and F distributions are sketched. 6 points
2. Complete an Analysis of Variance Table. The sum of squares and the degrees of freedom are given to you. You then need to test the claim that the means are equal. This means finding the test statistic (from the ANOVA table, the critical value (from the F-table), and then making a decision). 8 points.
3. Data from a sample is given. Find the mean, standard deviation, median, and range. Given the way the sample was collected, identify the type of sampling used. Five parts. 14 points.
4. Essay question. Answer ONE of the following. 10 points.
1. Compare and contrast variation, variance, and standard deviation. You should, at a minimum, include a definition of variation and variance, how to convert from the variation to the variance, why we usually work with the standard deviation instead of the variance, how to convert from the variance to the standard deviation.
2. Explain the concept of the probability-value. You should, at a minimum, include a definition of the probability-value, explain the decision rules using the p-value, which distributions are best suited for the p-value approach, some of the benefits of the p-value approach.
3. Explain the Central Limit Theorem. You should, at a minimum, include the three parts of the CLT, when you use the CLT, and the formula for a z-score when using the CLT.
5. Identify the distribution that should be used in each situation. The six distributions used are the uniform, binomial, normal, student's t, chi-square, and F. Each is used at least once. Eight parts. 8 points.
6. Given a binomial experiment, including the values for n and p, find the mean, standard deviation, and probability of specific outcome(s). Three parts. Use the binomial program on the calculator for the last part. 6 points.
7. Find the mean, variance, and standard deviation for a probability distribution. 6 points.
8. Match the term best defined to the definition. Know the following definitions: Alternative Hypothesis, Binomial Experiment, Class Mark, Class Boundary, Conclusion, Confidence Interval, Confidence Limit, Continuity Correction, Correlation Coefficient, Critical Value, Decision, Degrees of Freedom, Hypothesis, Median, Midrange, Multinomial Experiment, Null Hypothesis, Parameter, Probability Distribution, Sample Size, Statistic, Test Statistic, Type I Error, Type II Error. Fourteen parts. 14 points.
9. Use normal probabilities to find a probability for an individual and for a mean of a group. Two parts. 6 points.
10. Find the sample mean from a confidence interval. Use a confidence interval to perform a two-tailed hypothesis test. Two parts. 4 points.
11. Find some simple probabilities. Four parts. 8 points.
12. Sketch the graph and find the normal probability. Four parts. 9 points.
13. Find critical values for a normal, student's t, chi-square, and F distributions using the critical value (Z0.10) notation. Four parts. 8 points.
14. Find the expected value of a game. Find the probabilities of events occurring by creating a table listing the outcomes. Two parts. 4 points.
15. Write a conclusion based on the prob-value. It's in the form, there is __________ evidence at the ______ level of significance to __________ the claim that (the original claim is stated). 3 points.
16. Work a test for independence. Find some of the expected frequencies, identify how many degrees of freedom there are, find the critical value, and write the decision. Three parts. 7 points.
17. Essay. Explain why deviations from the mean must be squared when finding the variation. Draw a figure to illustrate your explanation. 4 points.

Notes:

• The final is open notebook.