Chapter 8

CHAPTER 8 EXERCISES 1. Define the correlation. 2. Determine in each case whether the value of r, is significant at the 0.01 level of significance. a) n = 18 [ =.86 c) n = 20 0 = .46 b) n = 14 C =.58 d) n = 32 0 = .25 3. determine in each case whether the value of r is significant at the 0.05 level of significance. a) n = 28 =.91 C) n = 160 =.36 b) n = 12 Co = .28 d) n = 8 0 =.73 4. calculate r for the scores which ten students got in two tests in Calculus and College Algebra. Describe the degree of relationships between the sets of data. Calculus Test College Algebra Test (x) (V) 28 25 22 19 18 12 16 13 30 24 27 23 20 17 14 10 25 22 15 14 5. With references to the preceding exercise, test the null hypothesis r = o at the 0.05 level of significance.6. The following table shows the scores which nine students got in English Test and Botany Test English Test Botany Test (x) (y) 8 12 15 9 17 18 10 14 20 16 12 10 14 13 18 15 8 a) Compute for the value of Is b) How will you describe the relationship between the sets of data? 7. With reference to the preceding exercise, test for the significance of the computed Is at the 0.05 level of significance.8. An agriculturest is interested to know whether the height of an eggplant affects the number of fruits it can produced. Ten eggplants were chosen at random from his garden and the results recorded: Height (cm) No. of Fruits Produced (x) (y) 28 34 24 29 23 37 31 41 22 25 27 35 29 39 26 33 25 27 a) Compute for the value [ b) Described the relationship between the height and the number of fruits produced by the eggplant. 9. With reference to the preceding exercise, test the significance of the computed [ at the 0.05 level of significance. 10. Compute for the value of r for the given data in number 8 and use the t-ratio to test the null hypothesis r = 0, at the 0.01 level of significance.10. Compute for the value of r for the given data in number o and use the f-ratio to test the null hypothesis r = 0, at the 0.01 level of significance. Set A: 1. Final the value of y in each of the following equation y = mx + b a) x = 8 m = 0.2518 b = 6 b) x =5 m = 3 b = 7 c) x = 0.1236 m = 0.3185 b = 0.5612 d) x = 0.3982 m = 2.1035 b = 1.3264 2. Construct a scatter diagram and draw a line that best fit for each of the following pairs of values. a) x 1 6 1 3 | 4 1 1 : 5 1 9 1 7 1 2 Y 1 8 1 6 1 8 1 8 | 10 | 11 1 9 1 12 bj x 1 711I 5 9 1 1 6 i 2 Y13 18 15 1 12 1 5 5 1 9 1 10 3. Use the given paired data to find the equation of the regression line. a) x 1 31 1|21 1 y 13 1 1 15 4 b) x1 1 3 1 41 6 1 8 1 y | 5.0 I 7.5 | 11.3 | 149 | 19.3 14. The following statistics are summarized from paired data find the best predicated value of y when x = 9 9) When the equation of the regression line is Y= 3.0x + 4.5 b) When the equation of the regression line is )= 5.02x -0.65 c) When the equation of the regression line is XAN = 1.2x + 16.7 5. The following statistics are collected and summarized from a study of the factors affecting success in differential and Integral Calculus for & randomly selected B.S. Math students. X is the score obtained in algebra placement test while y is the score obtained in calculus achievement test. Ex = 165 Ex,= 1334 Xxxx = 20,611 Xx" = 3855 Zy = 241,394 Exx = 29.611 x = 20 625 y = 166.75 3) Find m and b in the linear regression equation y = path bj If a student got a score of 40 in Algebra, what will be his score in Calculus? B. Use the given data in number 5 and compute the Se 7. The following table shows the length of employment that six employees at an electronic inspection department, and the number of components each of them have checked between 1:00 pm and 2:00 pm every Thursday. Number of weeks employed No. of components checked (xx) (y) 15 16 14 12 21 7 19 23 9) construct a scatter diagram. b) Find the equation of the regression line. c) Sketch the graph of the regression line in the scatter diagram. d) Compute the standard error of estimate. e) If a person has worked at the inspection department for 8 weeks, how many components can we expect him to inspect during the given period?8. The following are the number of years that 10 jobs applicants for employment abroad have studied College and their scores in a proficiency test in English. Number of years in College Proficiency Scores in English (X) (y) 84 63 48 75 78 OIAAGNAGNOU 58 57 72 73 89 a) Construct a scatter diagram. b) Find the equation of the regression line. c) Sketch the graph of the regression line in the scatter diagram. d) Compute for the standard error of estimate (se). e) If a student had studied 4 1% years in College, what will the approximate proficiency score