1. In hilly areas, farmers often contour their fields to reduce the erosion due to water flow. This might have the unintended effect of changing the yield since the rows may not be aligned in an east-west direction to take advantage of direct sunlight. The following summary statistics show the yields in hundreds of bushels per acre of randomly selected plots of land along hillsides as well as on level plots of land nearby with similar soil characteristics. For the hilly areas, assume that the largest three yields are 98.3, 99.1, and 100.01. For the level areas, assume the largest three yields are 125.8, 126.3, and 128.0. (a) Draw side-by-side box plots that show the yields of the two types of land. Check for outliers before making the plots. May 22-7:30 AM (b) Describe the shape and any unusual features of each plot separately. USE THE FLOWCHART! (c) Based on your box plots, what can you conclude about the different types of land? How are the box plots similar. Which type of land will most likely produce the highest crop yield in bushels per acre. May 22-7:32 AM 1
2. In some countries there are no primary elections to narrow down the field of candidates so several candidates could run for a particular office. If a candidate does not receive a majority, then the two candidates with the most votes run against each other in a run-off election a few weeks later. Suppose that there are three candidates: Candidate A, Candidate B, and Candidate C. Also suppose that each one comes from a different region of the country: Region 1, Region 2, and Region 3. Candidate A is from Region 1. Based on previous results, Region 1 casts about 35% of all votes in the country. Polls indicate that Region 1 will cast about 70% of its votes for Candidate A, 20% for Candidate B, and 10% for Candidate C. Candidate B is from Region 2. Based on previous results, Region 2 casts about 50% of all votes in the country. Polls indicate that Region 2 will cast about 20% of its votes for Candidate A, 60% for Candidate B, and 20% for Candidate C. Candidate C is from Region 3. Based on previous results, Region 3 casts about 15% of all votes in the country. Polls indicate that Region 3 will cast about 25% of its votes for Candidate A, 15% for Candidate B, and 60% for Candidate C. (a) If the actual vote is in line with the preliminary estimates, will one of the candidates receive a majority of the votes? If not, which two candidates will be in the run-off election? Show your work that leads to your conclusion. Draw a tree diagram. (b) What proportion of his total vote did Candidate C receive from his home region? May 22-7:33 AM 3. The table below gives the distribution of students at a certain high school for two categorical variables, grade year and the student s answer to the question. Do you eat regularly in the school cafeteria? Directions: Use correct notation. Show your arithmetic. State your answer in decimal (4 places). a) What is the probability that a randomly selected student eats regularly in the cafeteria? b) What is the probability that a randomly selected student is in the 10th grade? c) What is the probability that a randomly selected student is in the 10th grade and eats regularly in the cafeteria? d) What is the probability that a randomly selected student is in the 10th grade or eats regularly in the cafeteria? e) What is the probability that a randomly selected student eats regularly in the cafeteria, given that he or she is in the 10th grade? f) What is the probability that a randomly selected student is in the 12 th grade, given that he or she eats regularly in the cafeteria? g) If you choose a student at random, are the events 10th grade and eats regularly in the cafeteria independent? Explain how you know. May 22-7:35 AM 2
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May 22-10:50 AM Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations: 5. The scatterplot below displays the price in dollars and the quality rating for 14 different sewing machines. (a) Describe the nature of the association between price and quality rating for the sewing machines. (b) One of the 14 sewing machines substantially affects the appropriateness of using a linear regression model to predict quality rating based on price. Report the approximate price and quality rating of that machine and explain your choice. May 22-10:50 AM 4
(c) Chris is interested in buying one of the 14 sewing machines. He will consider buying only those machines for which there is no other machine that has both higher quality and lower price. On the scatterplot reproduced below, circle all data points corresponding to machines that Chris will consider buying. May 22-10:52 AM May 22-10:53 AM 5