HARDMAN MAT 2170 Review for Final Exam 1. Know the definitions of the following terms: A. Margin of Error B. Mean C. Range D. Parameter E. Continuous F. Outliers G. Scatterplot H. Mutually Exclusive I. Statistic J. IQR K. Median L. Correlation M. Sample Space N. Standard Deviation O. Independent P. Quartiles Q. Boxplot R. Event S. Discrete 2 2. DRAW THE APPROPRIATE PICTURES, and calculate each of the following probabilities. (3 points each) a. P [ 1.33 T ( 17) 2.567 ] b. P [ 0.61< Z <2.39 ] 3. Suppose that X~Bin(12, 0.4): a. Calculate the probability that X = 8 b. Calculate P [ 5< X 8 ] (5 points) (5 points) 4. Assume that you will take a sample of size 36 from a population of GPAs with a mean value of 2.1 and a population standard deviation of 0.4. a. Specify the sampling distribution of b. Calculate >2.20 ] . (4 points) P[X X , your sample mean value. (6 points) 3 5. Suppose that you do know the value of the population standard deviation and that you want to calculate an 80% CI for , the population mean value. Determine the value of the critical number that you would use to calculate this CI. (4 points) 6. Given the following probability distribution table for the random variable X: X: -3 f(x): 0.3 2 0.5 7 0.2 a. Calculate the Expected Value of X. (6 points) b. Calculate the Variance of X. (6 points) 7. Given the following heights measured in inches: 68, 72, 65, 69, 72: a. Calculate the mean height for this sample. (2 points) b. Calculate the standard deviation for this sample of heights. (4 points) 4 8. Suppose that you will pick two cards from a standard deck of 52 cards, without replacement, and you are only interested in whether each of the cards that you select is a diamond, or not. a. Draw the complete tree diagram, with all of the twig probabilities in place. (5 pts) b. What is the probability that exactly 1 of the two cards that you select is a diamond? (5 points) 9. Use the data set in question 7 to find the 95% CI for . (6 points) 10. Name the two desirable properties for any CI. (4 points) 5 11. Students were given a quiz, and the amount of time (measured in minutes) it took each student to finish the quiz was recorded. The results follow: 10, 11, 11.25, 12.5, 12.5, 14, 15, 18, 18, 20, 22 a. Complete the 5-Number summary of this data set: (3 points) Min: _______ Q1: _______ Q2: _______ Q3: _______ Max: _______ b. Calculate the IQR for this data set. (2 points) c. Calculate the Upper Fence for this data set. (2 points) d. What is the reason that you would calculate the Fences in an analysis? (2 points) 12. Calculate the sample size required to produce a 90% CI for an acceptable margin of error, E, is 1.25. (3 points) if =14.9 and 6 13. Consider the following scatterplots: (3 points each) 6 5 5 4 4 3 3 2 2 1 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 4 3 2 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 #1 #2 a. Which scatterplot has the smallest r-value? b.Which scatterplot shows the weakest linear correlation? c. Which scatterplot has an r-value closest to 1? #3 7 14. Assume that you ran the following hypothesis test: H O : 98 H A : <98 points)