# Math 113: Study Guide - Chapters 5-6

Problems 1-48 are true or false. Here are some of the things you need to know (not necessarily in question order). When I write "properties" of a distribution, I include mean, variance, standard deviation, requirements for use, symmetry, degrees of freedom, whether or not the critical values can be negative, and other items discussed in class or in the textbook.

• Know which distributions (uniform, binomial, normal, t, chi-square) are symmetric about their mean.
• Know which distributions require degrees of freedom.
• Know the properties of the uniform distribution.
• Know properties of normal distributions.
• Know properties of the standard normal distribution.
• Know properties of the Student's t distribution including who developed it and the relation of the student's t to the normal.
• Know properties of the chi-square distribution.
• Know properties of the sampling distribution of the sample means.
• Know which distribution is appropriate for the described situation. For example, flipping coins uses a binomial distribution; rolling a die uses the uniform distribution.
• Know the best point estimate for the population mean, proportion, variance, and standard deviation.
• Know the effects of increasing or decreasing the sample size, standard deviation, and confidence level on the maximum error of the estimate. From lab.
• Know what a confidence interval means and doesn't mean.
• Know the definitions of unbiased estimator, consistent estimator, relatively efficient estimator, finite population correction factor.
• Know when the binomial distribution can be approximated using the normal distribution.
• Know the different techniques for determining normality
• Know the empirical rule and Chebyshev's rule.

Here is a problem by problem description for the rest of the test.

1. Describe the difference between a standard normal and a non-standard normal distribution.
2. Identify the distribution from the graph. Need to know what the uniform, binomial, normal, Student's t, and chi-square distributions look like.
3. 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!
4. A uniform distribution is described. Draw the probability density curve, find the mean, and the probability of x lying between two values. Look at pages 227-228 and problems 5.2.1-8.
5. A confidence interval for the population mean is given. Find the sample mean and the margin of error. Look at page 305 and problems 6.2.1-4.
6. A confidence interval for the population proportion is given. Find the sample proportion and the margin of error. Look at page 336 and problems 6.5.1-4.
7. Use Statdisk to estimate a sample size.
8. Find a normal probability. Section 5.3.
9. Find the probability of a mean being a certain value using normal probabilities. Section 5.5.
10. Find a raw score using normal probabilities. Section 5.4.
11. Use Statdisk to construct a confidence interval.
12. Use Statdisk to construct a confidence interval.
13. Look at a qq-plot (normal probability plot) and determine if the data is normally distributed.

## Notes:

• Questions 1-48 are true/false and are worth 0.5 points each. Don't waste a lot of time on any one problem since the rest of the in-class test is worth 61 points.
• Problem 51 is extremely important (over 1/5 the points for the test)
• Give probabilities as decimals, not percents like the textbook.
• There is a take home portion of the exam using Minitab and Excel that is worth 15 points.
• A standard normal table will be supplied for you with the exam.

## Points per problem

 # Pts 1-48 49 50 51 52 53 54 55 56 57 58 59 60 61 Take Home Total 24 2 2 21 3 4 4 4 4 4 4 4 4 1 15 100

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Last updated February 13, 2003 11:23 PM