Stat 145 ? Final Exam Review Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember. Here are the five-number summaries for each group: n Min Q1 Median Q3 Max Rap 29 5 8 10 12 25 Mozart 20 4 7 10 12 27 None 13 8 9.5 13 17 24 Describe the W?s for these data. Name the variables and classify each as categorical or quantitative. Based on the following parallel boxplots and the five-number summaries, write a few sentences comparing the performances of the three groups. Here is a histogram of the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S. Department of Agriculture: The summary statistics for these data are: EMBED Equation.DSMT4 SD Min Q1 Median Q3 Max 48.4 3.50 42 45 49 52 53 Which summary statistics are most appropriate to use for these data? Explain. Write a few sentences about this distribution. Here is a scatterplot, Data Desk regression output, and a residual plot for the Midterm1 and Midterm2 scores of students in a class: EMBED MtbGraph.Document EMBED MtbGraph.Document Describe the association between Midterm2 and Midterm1 scores. Why would we use Midterm1 as the explanatory variable and Midterm2 as the response variable? What is the value of the correlation coefficient between Midterm2 and Midterm1 scores? What does it mean for a student to have a positive residual? How much of the variability in Midterm2 scores is explained by the regression on Midterm1 scores? Write the equation of the regression line. Predict the Midterm2 score of a student who earned 80 on Midterm1. Does it seem reasonable to make this prediction? Explain. Over what range of Midterm1 scores is it valid to use the regression line to predict Midterm2 scores? Explain. Based on the residual plot, does it seem that linear regression is appropriate here? Explain. A consumer organization estimated that 29% of new cars have a cosmetic defect such as a scratch or a dent when they are delivered to car dealers. This same organization believes that 7% have a functional defect?something that does not work properly?and that 2% of new cars have both kinds of problems. If you buy a new car, what?s the probability that it has some kind of defect? What?s the probability it has a cosmetic defect but no functional defect? If you notice a dent on a new car, what?s the probability it has a functional defect? Are the two kinds of defects disjoint events? Explain. Do you think the two kinds of defects are independent events? Explain. Avoiding an accident when driving can depend on reaction time. That time, measured from the moment the driver first sees the danger until he or she gets his or her foot on the brake pedal, is thought to follow a Normal model with a mean of 1.5 seconds and a standard deviation of 0.18 seconds. Suppose we sample one driver at random. What is the probability that this driver will have a reaction time less than 1.25 seconds? What is the probability that this driver will have reaction a time between 1.6 and 1.8 seconds? Suppose we have a random sample of 16 drivers. What is the probability that the mean reaction time for these drivers will be less than 1.25 seconds? What is the probability that the mean reaction time for these drivers will be between 1.6 and 1.8 seconds? Explain the difference between parts a and b above. A Rutgers University study released in 2002 found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had cheated at least once. Create a 99% confidence interval for the level of cheating among high school students. Make sure to check appropriate conditions and to interpret your interval in context. Would a 95% confidence interval be wider or narrower? Explain without actually calculating the interval. If we were to do a follow-up study and wanted to determine the proportion of students who had cheated at least once to within 1% with 99% confidence, how many people should we poll? Assume we have the Rutgers study data as a starting point. Vineyard owners have problems with birds that like to eat the ripening grapes. Grapes damaged by birds cannot be used for winemaking (or much of anything else). Some vineyards use scarecrows to try to keep birds away. Others use netting that covers the plants. Owners really would like to know if either method works and, if so, which one is better. One owner has offered to let you use his vineyard this year for an experiment. Propose a design. Carefully indicate how you would set up the experiment, specifying the factor(s) and response variable. The Centers for Disease Control say that about 30% of teenagers smoke tobacco (down from a high of 38% in 1997). A college has 522 students in its freshman class, 180 of whom report that they smoke tobacco. Is this evidence that more than 30% of the students at this college smoke tobacco? The Gallup Poll conducted a representative telephone survey during the first quarter of 1999. Among their reported results was the following table concerning the preferred political party affiliation of respondents and their ages. Party Rep Dem Ind Total 18-29 241 351 409 1001 Age 30-49 299 330 370 999 50-64 282 341 375 998 65+ 279 382 343 1004 Total 1101 1404 1497 4002 Find the probability that a randomly selected person is under 30 or over 65. Find the probability that a randomly selected person is an Independent. Find the probability that a randomly selected person is an Independent and under age 30. Find the probability that a person is an Independent who is under age 30. Find the probability that a person under age 30 is an Independent. Do you think party affiliation is independent of the voter?s age? Explain. (Do only in quarters when Chapter 23 is covered.) How large are hamster litters? Among 47 golden hamster litters recorded, these were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter. Create and interpret a 95% confidence interval. A friend claims that he heard a report that hamsters have an average of 7 baby hamsters per litter. Do these data support your friend?s claim? Conduct a hypothesis test, making sure to check all conditions and to put your conclusion into context. Could you have answered part b without conducting a hypothesis test and, instead, using your confidence interval from part a? Would you have gotten the same results? Explain. PAGE PAGE 3
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