# Study Guide - Final 2

## Math 113

1. Find the mean, median, range, midrange, mode, and standard deviation for a set of data. The data has been ranked to make finding the median and mode easier.
2. The mean and variance of a binomial distribution are given. Find n, p, and q.
3. A probability distribution (not binomial) is given. Find the mean, variance, and standard deviation.
4. You are told how many items are in a bag and then asked some simple probability questions based on this information.
5. You are given the observed frequencies in a contingency table and are asked to find some of the expected frequencies (not all of them), to identify the degrees of freedom, and to formulate a decision based on the given test statistic. You will need to know how to find the critical value.
6. You are asked to find the critical values for a Normal, Student's t, Chi-Square, and F distribution using the alpha notation. Be aware that for any of the distributions, if the alpha is greater than 0.5, it is actually a left tail value.
7. Given a variable with a binomial distribution (n and p given), find the probability of "at least" some value using the binomial table (A1). Then approximate the value using the normal approximation to the binomial. This is where the continuity correction factor must be applied.
8. Find the probability of an individual score from a normal population being between two numbers. Find the probability of the mean of a sample from that population being within the same two values.
9. Determine the sample mean from a confidence interval for the population mean. Use the confidence interval to conduct a two-tailed hypothesis test.
10. Shade the region included for six (6) normal probabilities with mean 0 and standard deviation 1. Then find the area under the curve (equal to the probabilities).
11. Find the expected value of a probability distribution.
12. Write the null and alternative hypotheses for six (6) situations. The situations are described in English, you need to convert them to math. For two sample situations, define the samples (women=1, men=2) or differences (d=before-after).
13. Linear correlation and regression. Summary statistics are given including n, sum of x, sum of y, SS(x), SS(y), and SS(xy). Compute the linear correlation coefficient r. Test the claim that their is significant linear correlation by 1) writing the null and alternative hypotheses, 2) look up the critical value (know what to do when the n isn't in the table), and 3) write the decision - not conclusion. Then write the regression equation y'=ax+b by 1) finding a, 2) x bar and y bar, and 3) b. Finally, estimate the dependent variable for a specific value of the independent variable. Note - only use the regression equation if there is in fact significant linear correlation. If there isn't, then the best estimate is y bar.
I urge you to put this sheet in the front of your notebooks with references to which sections to go to for each question. You may also want to tab (or separate in some manner) the sections which will be referenced. Review the questions from former tests like the ones that will appear here, and make sure that you know how to work them. If you need additional practice, go back to those sections in your textbook.