Statistics Exam Review: Final Exam Preparation for Statistics 1300, Exams of Statistics

Download Statistics Exam Review: Final Exam Preparation for Statistics 1300 and more Exams Statistics in PDF only on Docsity! Learning Center’s Statistics 1300 Final Exam Review Middlebush Room 12 Friday, May 8, 2009 2:00 – 4:00 p.m. Note 1: In addition to these review problems, I would advise students to work through problems from the sample finals posted on Blackboard. Note 2: There will be a Q&A session on Tuesday, May 12 from 12:00 to 1:30 p.m. in Middlebush 206. 1. A student’s final grade can sometimes be affected in a negative way by missing too many classes throughout a semester. To analyze the notion that the more days a student misses (x), the lower your final grade (y, in percentage), the data below were collected from a random sample of 10 students. x 2 1 10 5 25 12 7 40 22 0 y 84 95 85 75 54 58 81 70 62 91 2 2124, 755, 3032, 58797, 8265x y x y xyΣ = Σ = Σ = Σ = Σ = a) Find the equation of the least squares line. b) What final grade percentage should be predicted for a student who misses 9 classes? c) Find the sample correlation coefficient. d) Assuming that, for each value of x, the corresponding y’s have the same variance, find the estimate for this common variance. 2. Six subjects were selected at random, and the age and systolic blood pressure for each was recorded. Their ages ranged from 43 to 70, and their blood pressures ranged from 120 to 152. Using this data, Minitab produced the regression analysis output that is given below. Regression Analysis: Pressure versus Age The regression equation is Pressure = 81.0 + 0.964 Age Predictor Coef SE Coef T P Constant 81.05 13.88 5.84 0.004 Age 0.9644 0.2381 4.05 0.015 S = 5.641 R-Sq = 80.4% R-Sq(adj) = 75.5% Analysis of Variance Source DF SS MS F P Regression 1 522.21 522.21 16.41 0.015 Residual Error 4 127.29 31.82 Total 5 649.50 a) If we test the hypothesis 0 1: 0H β = against 1: 0AH β ≠ , what is the p-value for the test? b) Using .05α = , what would we conclude for the test in (a)? c) If we test the hypothesis that blood pressure tends to increase with age, what is the p-value for the test? 3. Use the relative frequency histogram at the right to answer the following questions. Read all relative frequencies to the nearest 5%. a) If there are 80 observations in the data set, how many observations are between 30 and 50? b) Find the median. c) Based on the histogram, which should be larger, the mean or the median? Why? 4. Find the standard deviation of the following data set: {1, 4, 5, 9}. 9080706050403020100 30 20 10 0 C1 P er ce nt 5. Of the members of a particular Poker club, 60% play Hold ‘em regularly, 55% play Seven Card Stud regularly, and 30% play both Hold ‘em and Seven Card Stud regularly. a) If members are selected at random, what is the probability that he or she will play either Hold ‘em or Seven Card Stud regularly? b) Are the events “plays Hold ‘em regularly” and “plays Seven Card Stud regularly” independent? Explain. c) Are the events “plays Hold ‘em regularly” and “plays Seven Card Stud regularly” mutually exclusive? Explain. 6. Suppose that 20% of professional comedians quit performing by the time they are 40 years of age. a) If 15 professional comedians are selected at random, what is the probability that at least 5 will quit by age 40? b) If 16 professional comedians are selected at random, what is the probability that exactly 2 will quit by age 40? x 1 2 3 4 5 p(x) 0.2 0.3 0.3 0.1 0.1 7. Find the expected value and variance of the probability distribution at the right. 8. Scores from a statistics exam are normally distributed with a mean of 78 and a standard deviation of 6. a) What is the probability that a randomly selected student (who took that particular exam) will score above an 88? b) How high a score would a person need to be in the top 15% on this particular exam? 9. In a random sample of 200 Mizzou football fans, 160 said they were already excited about next year’s season of Tiger football. a) Find a 95% Confidence Interval for the true proportion of Mizzou football fans that are excited about the upcoming football season. b) To estimate the true proportion of Mizzou fans that are excited about the upcoming football season to within 0.04 with 95% confidence, what sample size is needed? 10. A random sample of 9 trips by a professor to the beautiful Isle of Capri casino yielded mean winnings of $22 with a standard deviation of $15. a) Find a 90% confidence interval for the professor’s average winnings. b) Based on the 90% confidence interval, should we be confident that the professor wins more than $15 on an average visit? Explain. 11. A random sample of 100 brand new Firestone tires has 13 defective tires, and a random sample of 120 brand new Goodyear tires yields 9 that are defective. a) Using α = 0.05, conduct a test to determine if the proportion of defective tires is different for the two brands. What should you conclude? b) Find the p-value of the test. Based on the p-value, what should you conclude? c) Using the same data, Minitab produced the output below. Does this output contradict the findings from parts a and b above? Explain. Test and CI for Two Proportions Sample X N Sample p 1 13 100 0.130000 2 9 120 0.075000 Difference = p (1) - p (2) Estimate for difference: 0.055 95% CI for difference: (-0.0260280, 0.136028) Test for difference = 0 (vs not = 0): Z = 1.35 P-Value = 0.176 Fisher's exact test: P-Value = 0.185 12. To decide whether a new type of bumper performs better in low-speed crashes, 6 cars with the new bumpers and 6 cars with the old bumper design were each randomly selected and crashed into a concrete wall at a speed of 5 miles per hour. The cost of repairing the damages is given in the table below. Your assistant did not know whether you wanted to look at each sample separately or at paired differences, so he did calculations both ways. New 127 168 143 165 122 139 144x 19.06s= = Old 169 150 147 186 168 164 164x = 14.21s = Difference 42− 4 18 − 21− 46 25− 20x = − 24.02s = − a) Decide what kind of test would be appropriate, and carry it out at the .05 level of significance. You may assume equal variances. b) Find the p-value for the test as accurately as possible. Would your conclusion in (a) be different if the level of significance was .01? Explain. c) With the same data, your assistant used Minitab to obtain the results below. Do his results contradict your findings in a and b above? Explain. Two-Sample T-Test and CI: New, Old Two-sample T for New vs Old N Mean StDev SE Mean New 6 144.0 19.1 7.8 Old 6 164.0 14.2 5.8 Difference = mu (New) - mu (Old) Estimate for difference: -20.00 95% CI for difference: (-41.63, 1.63) T-Test of difference = 0 (vs not =): T-Value = -2.06 P-Value = 0.066 DF = 10 Both use Pooled StDev = 16.8107