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Exam 2 1. 2. 3. Name: Load the data set physicians.xls. The data show the number of physicians of each sex working in each specialty. Construct a scatterplot of Women versus Men. Which specialty is an outlier? (a.) dermatology (b.) pediatrics (c.) plastic surgery (d.) radiology Open the data set planets.xls. Construct a scatterplot of Revolution versus Distance. Describe the direction, strength, and form of the association. (a.) positive, moderate, linear (b.) negative, moderate, linear (c.) positive, strong, nonlinear (d.) no relationship Calculate the correlation between Revolution and Distance. (a) -.02 (b) .55 (c) .99 (d) -55 4. Which of the following is NOT true about correlation? (a.) it is only appropriate to use correlation when the relationship is linear (b.) if the correlation coefficient is close to 1 or -1, there is a cause-and-effect relationship (c.) correlation is sensitive (not resistant) to outliers (d.) all of the above are true 5. 6. 7. Sampling variability is the concept that the results in a study will vary from sample to sample in random sampling. To reduce sampling variability, a researcher can… (a.) increase the sample size (b.) use resistant parameters (c.) make a dotplot (d.) use judgment instead The best possible procedure for using a sample for estimating a characteristic of a population is one that has: (a.) High bias and low variability (b.) Low bias and low variability (c.) Low bias and high variability (d.) High bias and high variability Below is the Statcrunch output for a linear regression. Simple linear regression results: Dependent Variable: SUGAR(mg) Independent Variable: SODIUM(mg) SUGAR(mg) = 13579.683 - 29.000984 SODIUM(mg) Sample size: 20 R (correlation coefficient) = -0.453 R-sq = 0.20525242 The slope of the regression equation indicates that… 8. (a) There is a strong negative linear relationship (b) There are 13,580 mg of sodium for every gram of sugar (c) An increase of 1 mg of sodium tends to go with a decrease in 29 mg of sugar. (d) None of the above The “line of best fit” under the least squares criterion is the one which… (a) minimizes the sum of all the perpendicular distances from the points to the line. (b) has the greatest sum of squared errors in predictions. (c) has the smallest sum of squared residuals (d) has the smallest average residual 9. It may be necessary to transform the data such as by computing logs or square roots on before performing a linear regression if… (a) (b) (c) (d) there are many outliers the scatterplot shows a nonlinear relationship there is no apparent relationship between the variables all of the above Consider the two-way table below based on a a class of 30 students and their responses as to whether or not they own a cat and whether or not they own a dog: 10. Total Has a Dog 8 4 12 No Dog 2 16 18 Total 10 20 30 80% 40% 33% 50% What proportion of students who own a cat also own a dog? (a.) (b.) (c.) (d.) 12. No Cat What proportion of students own a cat? (a.) (b.) (c.) (d.) 11. Has a Cat 80% 40% 33% 67% What proportion of students who own a dog also own a cat? (a.) (b.) (c.) (d.) 80% 40% 33% 67% 13. Describe the relationship between having a cat and having a dog in this class. (a.) whether a student has a dog is not related to whether the student has a cat (b.) Students with a cat are more likely to also have a dog than students without a cat (c.) Students with a dog are less likely to have a cat than students who do not have a dog (d.) Most students have either a cat or a dog or both 14. Based on the segmented bar graph, the proportion of Women who prefer Dance is about… (a.) 11% (b.) 20% (c.) 50% (d.) 64% 15. The proportion of Men who prefer Sports is about… (a.) 10% (b.) 20% (c.) 50% (d.) 70% 16. The following data is based on a survey of students' smoking habits taken in eight Arizona high schools comparing smoking and nonsmoking teens based on whether both parents, one parent or neither parent is a smoker: smoker non smoker Total both parents smoke 400 1380 1780 one smokes 416 1823 2239 neither smoke 188 1168 1356 1004 4371 5375 Total Use the pie charts below to decide which of the following is NOT true about the relationship between whether a teen smokes and whether both, one, or neither of their parents smoke. (a.) Non-smokers are more likely to have parents who both do not smoke than smokers (b.) Both smokers and non-smokers have about just as likely to have one parent who smokes (c.) Non-smokers parents are usually non-smokers (d.) Smokers are more likely to have parents who both smoke than non-smokers SMOKERS NON-SMOKERS 17. Characteristics of a population are called ________, while those of a sample are termed _________. (a.) statistics; measures (b.) parameters; statistics (c.) statistics; variables (d.) statistics; parameters 18. Suppose we are interested in the average math PSSA scores for Haverford High School juniors. The set of all juniors at Haverford High School would comprise the ________ while the set of all juniors in Mr Peterson’s block 3 class is a __________. (a.) statistic; sample (b.) sample; parameter (c.) statistic; parameter (d.) population; sample 19. In a study of eating habits among Haverford High School teachers it was determined that 80% of ALL teachers prefer pizza to tacos. In a second study using a random sample of teachers, 50% of the teachers in the sample preferred pizza to tacos. The number 50% is a _________ while 80% is a _________. (a.) statistic; sample (b.) sample; parameter (c.) statistic; parameter (d.) population; sample Below is a list of names numbered 1 to 20. Use the random number table to randomly select 5 names from the list by starting at the beginning of the table and taking pairs of digits. 1 Sofia 11 Dara 2 Eassa 12 Jay 3 Jeffrey 13 Nicole 4 Shakoya 14 Francis 5 John 15 Audrey 6 Rebecca 16 Anthoula 7 William 17 Hiep 8 Johanna 18 Sean 9 Allyson 19 Shanira 10 Brandon 20 Alexis Table of random digits 11121 61998 32134 10012 99091 67743 11123 45672 04567 00998 20. What is the second name selected? (a.) Nicole (b.) Jeffrey (c.) Jay (d.) Allyson 21. What is the fifth name selected? (a.) Nicole (b.) Jeffrey (c.) Jay (d.) Allyson 22. Which of the following is really a simple random sample? (a.) The teacher wants to show a representative sample of student work, so she picks one good paper, one average paper, and one bad paper. (b.) The gym teacher asks the students to line up and count off by four’s. All the “one’s” are selected to be one team. (c.) The name of each person in the population is put into a hat and mixed well. Names are drawn from the hat without looking. (d.) The surveyor picks a sample of people he feels is representative of the population. 23. A grocer receives a shipment of apples in a large crate. In order to determine the proportion of apples that are bruised in the large crate of apples, she examines a sample of 20 apples taken from the top of the crate and notes that 5% are bruised. The sampling method could be said to be biased because… (a.) the apples in this crate may have been damaged during shipment (b.) this crate of apples may not be representative of all such crates (c.) she only looked at 20 apples, her sample is too small (d.) the proportion of apples that are bruised in the sample using only top apples is likely to be smaller than the proportion of apples that are bruised in the entire crate. 24. An experiment is conducted to determine if the use of certain specified amounts of a drug will increase IQ scores. In this study, IQ serves as: (a) an explanatory variable (b) a moderator variable (c) a response variable (d) a control variable 25. In order to test the effects of light level on student performance on tests, subjects are randomly assigned to two rooms to take a test. One room had a lower light level than the other. During the testing it was noted that one room’s temperature was 70 degrees whereas subjects in the other group are simultaneously tested in a nearby identically appointed room with the heat set at 60 degrees. A possible confounding variable in this study is… (a.) test score (b.) lighting level (c.) temperature (d.) random assignment 26. Researchers would like to understand how pet ownership is related to longevity. Which of the following is true? (a.) This study would be considered an observational study if they randomly assigned subjects to either receive a pet or not. (b.) This study would be considered an experiment if they randomly assigned subjects to either receive a pet or not. (c.)This study would be considered an experiment if they took a random sample of pet owners and noted whether or not they owned a pet (d.) none of the above is true 27. If the researchers in a study want to be able to conclude that watching television CAUSES poor academic performance and is not merely ASSOCIATED with school performance they need to… (a.) Conduct a well-controlled experiment (b.) Use an unbiased random sample in an observational study (c.) both (a.) and (b.) would be appropriate studies for the researchers (d.) neither of these types of studies can be used to establish a cause-and-effect relationship between watching TV and academic performance 28. The Physicians’ Health Study tried to find out if taking aspirin regularly helps prevent heart attacks and/or strokes. The subjects were 20,071 healthy male doctors at least 40 years old. The subjects were randomly divided so that one group took aspirin every other day and a second group took a placebo. The doctors in the aspirin group had far fewer heart attacks than those in the control group. This study is an… (a.) observational study, so it is reasonable to conclude that aspirin reduced risk of heart of attacks. (b.) observational study so it is inappropriate to draw cause and effect conclusions (c.) experiment so it is reasonable to conclude that aspirin reduced risk of heart of attacks. (d.) experiment so it is inappropriate to draw cause and effect conclusions 29. What is the role of randomization in an experiment? (a.) A random sample of subjects is selected from a population to avoid bias (b.) Subjects are randomly assigned to treatments so create experimental groups that are similar (c.) Treatments are applied to every subject at random intervals (d.) Experimenters must randomly decide what the purpose of the study is 30. The control group in an experiment should be designed to receive: (a.) the opposite of the experiences afforded the experimental group. (b.) the same experiences afforded the experimental group except for the treatment under examination. (c.) the experiences afforded the experimental group except for receiving the treatment at random intervals. (d.) the experiences which constitute an absence of the experiences received by the experimental group. 31. In an experiment to see if Smartfood Popcorn makes people smarter, 50 students are randomly assigned to two groups. The first group receives Smartfood popcorn and the second gets regular popcorn. Then each student writes an essay on an assigned topic. The essays are scored by a teacher and the results are compared for the two groups to see if Smartfood had a positive effect on essay writing. Which of the following would ensure blindness and double-blindness in this study? (a.) the students and reseachers should both wear blindfolds (b.) no one should know whether Smartfood was used for either group. (c.) the students should not know whether they got Smartfood or a different brand of popcorn, and the teacher should not know which group the the student was in while grading the essay. (d.) Smartfood should be given to both groups but in random intervals so that the students do not know when they are getting it 32. An experiment is said to take into account the principle of blindness if ___________, and it could be said to be double-blind if _____________. (a.) the subjects are randomly assigned to treatments; those evaluating the subjects are blindfolded (b.) the subjects are not aware of which treatment group they are in; those evaluating the subjects are not aware of which treatment group the subjects are in (c.) the subjects are selected at random from the population; those evaluating the subjects are not aware of which treatment group the subjects are in (d.) the subjects are not aware of which treatment group they are in; the two treatment groups are never come in contact 33. In an experiment studying the effect of a new drug for treating high blood pressure, the control group in the experiment should receive (a.) a lower dose of the drug (b.) nothing (c.) a placebo (d.) euthanasia 34. Consider an experiment to investigate the efficacy of different insecticides in controlling pests and their effects on subsequent yield. What is the best reason for randomly assigning treatment levels (spraying or not spraying) to the experimental units (farms)? (a) Randomization makes the experiment easier to conduct because we can apply the insecticide in any pattern rather than in a systematic fashion. (b) Randomization makes the analysis easier because the data can be collected and entered into the computer in any order. (c) Randomization is required by statistical consultants before they will help you analyze the experiment. (d) Randomization will tend to average out all other uncontrolled variables such as soil fertility so that they are not confounded with the treatment effects. 35. Researchers have observed that drinking red wine seems to lead to fewer men having heart attacks. More recently, others have noted that drinking red wine leads to headaches and people with headaches tend to take aspirin. Furthermore, aspirin is known to reduce the changes of having heart attacks. Given these facts, the relationship between drinking red wine and having heart attacks would be best described as confounded by the use of aspirin because (a.) the cause-and-effect relationship between aspirin and reducing the risk of heart attacks can be inferred from this study while the effect of drinking wine cannot (b.) aspirin was not a variable measured in the study and was not controlled for in the study but could affect the response variable (c.) it may be that heart attacks cause people to drink wine instead of the other way around (d.) there is a placebo effect at work in this experiment. 36. Which of the following is a confounding variable? (a.) a variable which was not measured but may explain the relationship between the variables that were measured (b.) a response variable that may also be thought of as explanatory (c.) a placebo (d.) any variable could be considered confoundin 37. Which is NOT a correct interpretation of the Law of Large Numbers? 38. (a.) If you flip a coin 10 times we expect to get 5 “heads” on average (b.) If you flip a coin a large number of times you are more likely to get close to 50% “heads” than if you flip a coin a small number of times. (c.) If you flip a coin twice and get “heads” both times, the next flip will most likely come up “tails” (d.) If you flip a coin 50 times, you probably won’t get exactly 25 “heads” but you are likely to get somewhat close to 50% “heads” Which of the following is NOT a possible probability? (a.) 25/100 (b.) 1.25 (c.) 1 (d.) 0 39. Tina has 5 red, 6 blue, 3 white, and 4 orange marbles. All marbles are put in a sack and one marble is selected at random. Compute the probability of drawing a red marble and the probability of drawing a blue or white marble. (a.) 4/19; 9/20 (b.) 3/10; 11/20 (c.) 5/18; 1/2 (d.) 9/21; 7/18 40. 41. A die is rolled. If the number rolled is odd, Player A wins $2 from Player B. If it is a 6, A wins $4 from B. Otherwise B wins $5 from A. Is this a fair game? (a.) Yes, because the expected value is 0. (b.) Yes, because the expected value is positive for player A (c.) No, because the expected value is negative for player A (d.) No, because the expected value is 0 When rolling a pair of 6-sided dice, what is the probability of rolling a sum of 7? (a.) 1/6 (b.) 3/14 (c.) 5/12 (d.) 11/36 42. Tina has 5 red, 6 blue, 3 white, and 4 orange marbles. All marbles are put in a sack and one marble is selected at random. Compute the probability of drawing a red marble and the probability of drawing a blue or white marble. (a.) 4/19; 9/20 (b.) 3/10; 11/20 (c.) 5/18; 1/2 (d.) 9/21; 7/18 43. Which is a correct interpretation of the Law of Large Numbers? (a.) If you flip a coin 10 times and get 9 heads, we expect to get tails on the next toss. (b.) If you flip a coin a small number of times you are more likely to get close to 50% “heads” than if you flip a coin a large number of times. (c.) If you flip a coin twice and get “heads” both times, the next flip will most likely come up “tails” (d.) If you flip a coin 50 times, you probably won’t get exactly 25 “heads” but you are likely to get somewhat close to 50% “heads” 44. Use StatCrunch to calculate the correlation between position and price. (a) 39.84 (b) 8.42 (c) .99 (d) .88 45. Use StatCrunch to calculate the linear regression equation of price versus position. Which of the following is an appropriate interpretation of the slope of the regression equation? (a) Every increase in price of one dollar tends to be associated with an increase in one position (b) There is a rise of 39.84 and a run of 8.42 (c) The position is unrelated to the price (d) An increase in one position tends to go with an increase in price of $8.42 46. What is the y-intercept? (a) 39.84 (b) 8.42 (c) .99 (d) .88 47. If there were a 23rd property, what price would be predicted by the regression equation for this new property? (a) $233.52 (b) $15.71 (c) $1912.43 (d) $23.23 48. Calculate the linear regression of rent versus price. (Note that price is the explanatory variable and rent is the response.) (a) price = -3.2 + .2011(rent) (b) rent = -4.7 + .1055(price) (c) price = 2.3 + .2110(rent) (d) rent = 7.4 + .5501(price) 49. 50. A negative residual value indicates that… (a.) the average error is greater than the predicted error (b.) the predicted value is greater than the observed value (c.) the observed value is greater than the predicted value (d.) the error in y is explained by x A certain random event only two possible outcomes, A and B. If the probability that A happens is .2, then the probability that B happens is (a) .8 (b) .5 (c) .2 (d) cannot be determined