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math221f2008quiz3
Course: MATH 221, Fall 2009School: Syracuse
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221 MAT Fall 2008 Quiz 3 (1.3, 2.1, 2.2, 2.3) Name 1. Using either Table A or your calculator or software, nd the proportion of observations from a standard Normal distribution that satises each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question. (a) Z < 1.65 (b) Z > 1.65 (c) Z > 0.76 (d) 0.76...
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221 MAT Fall 2008 Quiz 3 (1.3, 2.1, 2.2, 2.3)
Name
1. Using either Table A or your calculator or software, nd the proportion of observations from a standard Normal distribution that satises each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question. (a) Z < 1.65 (b) Z > 1.65 (c) Z > 0.76 (d) 0.76 < Z < 1.65 2. Each of the following statements contains a blunder. Explain in each case what is wrong. (a) There is a high correlation between the gender of American workers and their income. (b) We found a high correlation (r = 1.09) between students ratings of faculty teaching and ratings made by other faculty members. (c) The correlation between planting rate and yield of corn was found to be r = 0.23 bushel. 3. In Prof. Means statistics course the correlation between the students total scores before the nal exam and their nal exam scores is r = 0.55. The pre-exam totals for all students in the course have mean 270 and standard deviation 30. The nal exam scores have mean 70 and standard deviation 9. Prof. Mean has lost Conors nal exam but know that his total before the exam was 310. She decides to predict his nal exam score his from pre-exam total. (a) What is the slope the least-squares regression line of nal-exam scores on pre-exam total scores in this course? What is the intercept? (b) Use the regression line to predict Conors nal exam score. (c) Conor doesnt think this method accurately predicts how well he did on the nal exam. Calculate r2 and use the value you get to argue that his actual score could have been much higher or much lower than the predicted value. 4. The number of people living on American farms has declined steadily during the past century. Here are data on the farm population (millions of persons) from 1935 to 1980: Year Population 1935 32.1 1940 30.5 1945 24.4 1950 23.0 1955 19.1 1960 15.6 1965 12.4 1970 9.7 1975 8.9 1980 7.2
(a) Make a scatterplot of these data and nd the least-squares regression line of farm population versus year. (b) According to the regression line, how much did the farm population decline each year on the average during this period? (What is the slope?) What percent of the observed variation in farm population is accounted for by linear change over time? (What is r2 ?). (c) Use the regression equation to predict the number of people living on farms in 1990. Is this result reasonable? Why?
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