## Math 113: Study Guide - Chapters 5-6

1. Four binomial distributions with different p values are given. Match the distribution to the graph. Know that the mean of a binomial is np.
2. Four student t distributions with different degrees of freedom are given. Match the distribution to the graph. Know what happens as the sample size increases.
3. Four chi-square distributions with different degrees of freedom are given. Match the distribution to the graph. Know what happens when the sample size increases.
4. Know which distributions (uniform, binomial, normal, t, chi-square) are symmetric about their mean
5. Know which distributions require degrees of freedom
6. Know properties of the standard normal distribution (multiple choice)
7. Know properties of the Student's t distribution (multiple choice)
8. Know properties of the chi-square distribution (multiple choice)
9. Know properties of the sampling distribution of the sample means (multiple choice)
10. Know which distribution is appropriate for the described situation. For example, flipping a coin uses a binomial distribution; rolling a die uses the uniform distribution.
11. Know which distribution is appropriate.
12. Know the best point estimate for the population mean
13. Know the best point estimate for the population proportion.
14. Know the best point estimate for the population variance.
15. Know the effect of increasing or decreasing the sample size on the maximum error of the estimate. From lab.
16. Know the effect of increasing or decreasing the level of confidence on the maximum error of the estimate. From lab.
17. Know what a confidence interval means.
18. Look up a critical z-score using the alpha notation. Z0.10 means the z-score with 0.10 area to the right which is 1.282.
19. Look up a critical t-score using the alpha notation.
20. Look up a critical chi-square score using the alpha notation. Know how to handle degrees of freedom that aren't in the table.
21. Given a confidence level and a critical value from the t-table, find the sample size. Remember that the t-table gives degrees of freedom, you will need to add 1 to get the sample size.
22. Know the difference between a standard normal a non-standard normal distribution.
23. Find a normal probability (like section 5.3).
24. Find a raw score using normal probabilities. Like the competitive test problem 5.4.18.
25. Find the probability of a mean being a certain value using normal probabilities. Section 5.5.
26. Use a standard normal distribution to find probabilities. There are seven parts. You must draw the picture and find the probability. There is a normal graph given, you just need to shade the proper portion. Two points for finding the correct probability and one point for shading the proper region. This problem accounts for slightly over 1/5th of the points on the test and it is very important!
27. Matching. Know the definitions of consistent estimator, continuity correction factor, level of confidence, degrees of freedom, efficient estimator, finite population correction factor, interval estimate, maximum error of the estimate, point estimate, sampling distribution of the sample means, standard error of the mean, and unbiased estimator.
28. Identify the distribution from the graph. Need to know what the uniform, binomial, normal, Student's t, and chi-square distributions look like.
29. Use Statdisk to estimate the sample size.
30. Use Statdisk to find a confidence interval.
31. Use Statdisk to find a confidence interval.

### Notes:

• Problems 1-3 are matching and 4-25 are multiple choice. Problems 4-9 may have multiple responses.
• Be sure you bring your book to the test, you will need it for the tables.
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Pts 2 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 # 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Total Pts 2 2 2 2 2 2 2 2 2 21 10 4 3 3 3 100