Professor Gill has taught General Psychology for many years. During the semester

Question

Professor Gill has taught General Psychology for many years. During the semester, she gives three multiple-cholice exams, each worth 100 points. At the end of the course, Dr. Gill glves a comprehensive final worth 200 points. Let x1, *2, and xy represent a student's scores on exams 12, and 3, respectively. Let x4 represent the student's score on the final exam. Last semester Dr. Gan had 25 students in her class. The student exam scores are shown below 73 80 75 152 93 88 93 18S 89 91 90 180 96 98 100 196 73 66 70 142 53 46 55 101 69 74 77149 47 56 60 115 87 79 90 175 79 70 88 164 69 70 73 141 70 65 74 141 93 95 91 18 79 80 73 152 70 73 78 148 93 89 96 192 78 75 68 147 81 90 93 183 88 92 86 177 78 83 77 159 82 86 90 177 86 82 89 175 78 83 85 175 76 83 71 149 96 93 95 192 0 48 Since Professor Gill has not changed the course much from last semester to the present semester, the preceding data should be useful for constructing a regression model that describes this semester as well (a) Generate summary statistics, including the mean and standard deviation of each variable. Compute the coefficient of variation for each variable. (Use 2 decimal places.) cV x3 Relative to its mean, would you say that each exam had about the same spread of scores? Most professors do not wish to give an exam that is extremely easy or extremely hard. Would you say that all of the exams were about the same level of difficulty? (Consider both means and spread of test scores.) O No, the spread is different; Yes, the tests are about the same level of difficulity O No, the spread is different; No, the tests have different levels of difficulty O Yes, the spread is about the same; No, the tests have different levels of difficulty. O Yes, the spread is about the same; Yes, the tests are about the same level of difficulty. (b) For each pair of variables, generate the correlation coefficient r. Compute the corresponding coefficient of determination r2. (Use 3 decimal places.) x2, X3

Explanation / Answer

(a)

Option 3 is correct.
Yes, the spread is about the same. No, the tests have different levels of difficulty.

(b)

x s Cv x1 79.04 12.28 15.54 % x2 79.48 12.50 15.73 % x3 81.48 11.77 14.44 % x4 162.04 24.04 14.84 %

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