ANSWER ALL THE FOLLOWING EXERCISES
Exercises 11 - About Cramer's V
Exercises 12 - About Pearson Correlation Coefficient
Exercises 13- About Regression Analysis
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Exercises 11 (1) A random sample of 800 Marawi City residents are classified according to their economic status (such as low, middle, and high) and their opinions whether or not they are favor to the new re- routing scheme in Quezon Avenue. The observed frequencies are presented below: Decision Low Middle High For 152 183 143 Against 104 128 90 (a) Compute the percentage distribution of each income category. Which income category has the highest percentage against the re-routing scheme? (b) Compute the Cramer's V and interpret the result. (2) A researcher conducted a survey to determine whether working mother affect the performance of their 8 year old children in school. The following data were taken on a random sample of 200 8- year old students. Performance of 8 year old students in school Low Average High Working Mother 42 44 34 Non-working Mother 46 22 12 (a) Which do you think is the independent variable? Compute the percentage distribution and compare them. What do you observe? (b) Compute the Cramer's V and interpret the result.(3) A random sample of 200 married men, all retired, was classified according to education and number of children. Number of Children Education 0-1 2-3 Over 3 Elementary 14 37 32 Secondary 19 42 17 Tertiary 12 17 10 (a) Compute the percentage distribution of each level of educational attainment. Compare the results. (b) Compute the Cramer's V coefficient. Interpret the result.Exercises 12 1. A researcher wishes to see if there is a relationship between the number of calories a sandwich has and the sodium content of the sandwich. Several different types of sandwiches are used. The data follow (Source: Consumer Reports 60, no. 9, September 1995). Calories, x 419 419 386 240 354 231 174 Sodium (mg), y 495 645 1202 581 990 1159 787 2. A researcher wishes to determine if there is a relationship between the energy efficiency rating (EER) of an air conditioner and its cost. The EER is determined by the Appliance Manufacturers' Association (Source: Consumer Reports 60, no.6, June 1995, p.406). The data follow. EER, x 9.5 10.0 10.0 10.0 10.3 9.1 8.6 Cost ($), yl 370 360 400 400 420 350 310 3. An educator wants to see the relationship between a student's score on a test and his or her grade point average. The data obtained from the sample follow. Test score, x 98 105 100 106 95 116 112 GPA, y 2.6 2.1 2.3 2.0 2.4 1.7 1.9 4. An English instructor is interested in finding the strength of a relationship between the final exam grades of students enrolled in English 1 and English 2 classes. The data are given below in percentages. Check your answer in calculator. English 1, x 83 97 80 95 73 78 91 86 English 2, y 78 95 83 97 78 72 90 80Exercises 13 (1) In a study between the amount of rainfall (X, in .01 cm) and quantity of air pollution removed Y, micrograms per cubic meter), the following data were collected: X 4.3 4.5 5.9 5.6 6.1 5.2 3.8 2.1 7.5 Y 126 121 116 118 114 118 132 141 108 a) Find a linear equation relating X and Y. b.) Estimate the amount of air pollution removed when amount of rainfall is 4.7. c.) Estimate the amount of air pollution removed when amount of rainfall is 4.5. Compute the amount of cave between the actual observed value and the predicted value. (2) A physician wishes to know whether there is a relationship between father's weight (in pounds) and his newborn son's weight (in pounds). The data are given here. Father's weight, x 176 160 187 210 196 142 205 215 Son's weight, y 6.6 8.2 9.2 7.1 8.8 9.3 7.4 8.6 a.) Find a linear equation relating X and Y. b.) Estimate the amount of son's weight when the amount of father's weight is 7.9. Stat 33, Second Semester, A.Y. 2020-2021 Mathematics Dep't, MSU, Morowi City 16 c.) Estimate the amount of son's weight when the amount of father's weight is 8.2. Compute the amount of error between the actual observed value and the predicted value. (3) Suppose a study is to see whether there is a relationship between a student's grade point average and the number of hours the student studies per week. Predict the GPA of a student who studies 10 hours a week. The data are shown here. Check the answer in your calculator. Hours, x 3 12 9 15 5 7 16 GPA, y 2.5 3.0 2.75 1.75 2.25 1.0 4. A study is conducted to determine the relationship between a driver's age and the number of accidents he or she has over a year period. Predict the number of accidents of a driver who is 28. Check the answer in your calculator. The data are shown here. Driver's 16 24 18 17 23 27 32 age, x No. of 3 2 5 2 0 accidents, y
