Business Research Methods - Exam 2

A) boxplots make it easy to compare several distributions, as in this example.

10. Here are boxplots of the number of calories in 20 brands of beef hot dogs, 17 brands of meat hot dogs, and 17 brands of poultry hot dogs. *The main advantage of boxplots over stemp lots and histograms is that:* A) boxplots make it easy to compare several distributions, as in this example. B) boxplots show more detail about the shape of the distribution. C) boxplots use the five - number summary, whereas stemplots and histograms use the mean and standard deviation. D) boxplots show skewed distributions, whereas stemplots and histograms show only symmetric distributions.

A) 4

14. This boxplot shows the distribution of heights of 16 undergraduate statistics students. From the above boxplot, approximately how many students are 69 inches or taller? A) 4 B) 8 C) 12 D) 16 E) We can't say.

E) - 0.90

21. A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure. A plausible value of the correl ation coefficient for the data displayed is A) -0.40. B) - 0.25. C) 0.00. D) +0.75. E) - 0.90.

E) r = 0.85.

22. How well does the number of beers a student drinks predict his or her blood alcohol content? Sixteen student volunteers at The Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC). A scatterplot of the data appears below. *A plausible value of the correlation between number of beers and blood alcohol content, based on the scatterplot, is:* A) r = -0.85. B) r = -0.3. C) r close to 0. D) r = 0.3. E) r = 0.85.

A) larger houses cost more to heat than smaller houses, and the relationship is almost perfectly straight.

26. A study of home heating costs collects data on the size of houses and the monthly cost to heat the houses with natural gas. Here is the data: A friend tells you that the correlation for the data is r = 0.99984. You conclude from this number that: A) larger houses cost more to heat than smaller houses, and the relationship is almost perfectly straight. B) smaller houses cost more to heat than larger houses, and the relationship is almost perfectly straight. C) larger houses cost more to heat than sma ller houses, but the relationship is not very strong. D) smaller houses cost more to heat than larger houses, but the relationship is not very strong. E) your friend made a mistake, because the value of r is impossible.

B) change in days since last visit f or each year older a patient is, on average.

27. A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least- squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 -8.694x. The slope of this line tells us the A) correlation between age of patient and days since last visit. B) change in days since last visit f or each year older a patient is, on average. C) change in the age of the patient for each extra day since the last visit. D) average days since last visit for all of the patients.

C) 0.84 0.64 + 0.20 = 0.84

40. If an American household were chosen at random and asked how many tablet computers it owned, here are the probabilities as determined by a recent survey: What is the probability that a randomly chosen household owns fewer than two tablet computers? A) 0.20 B) 0.64 C) 0.84 D) 0.96 E) It is not possible to tell from the given information.

B) 1/6 3/36 + 2/36 + 1/36 = 6/36 1/6

41. In many popular board games, a player rolls two dice and moves the number of spaces equal to the sum shown on the dice. Here is the assignment of probabilities to the sum of the numbers on the up faces when two fair dice are rolled: Suppose Scott and Jennifer each rolls a sum of 9 on their first rolls. What is the probability that Quint will have a greater sum on his first roll? A) 0 B) 1/6 C) 1/12 D) 5/18 E) 1

C) No, it's smaller than 1/6 + 1/6. Count of Aces: 10/36 + 1/36 = 11/36 11/36 = 0.305 1/6+1/6 = 2/6 2/6 = 0.333 0.333 > 0.305 2/6 > 11/36 Therefore, the probability of a count of aces (11/36) is smaller than 1/6 + 1/6 = 2/6.

42. If we roll a pair of fair dice and count the number of aces (one dot) showing, the probability model is as follows: Back in the 17th century, some gamblers thought that the probability of at least one ace (i.e., one or more aces) when rolling two dice was 1/6 + 1/6. Is that true? A) Yes. B) No, it's larger than 1/6 + 1/6. C) No, it's smaller than 1/6 + 1/6. D) Sometimes it's larger and sometimes it's smaller. E) Impossible to say.

C) 0.23 4 or more people 0.14 + 0.06 + 0.02 + 0.01 = 0.23

44. A household is a group of people living together at the same address. According to the 2015 Current Population Survey's Annual Social and Economic (CPS ASEC) Supplement, if an American household were chosen at random and asked how many people lived there, here are the probabilities: What is the probability that a randomly chosen household contains four or more people? A) 0.09 B) 0.14 C) 0.23 D) 0.91 E) It is not possible to tell from the information given.

C) 0.52

45. Suppose flights at a large metropolitan airport are on - time 68% of the time and late 32% of the time. We want to use a table of random digits to simulate flight status (on - time or late), so we'll assign 01, 02, ... , 68 to represent on - time flights, and 69, 70, ... , 99, 00 to represent late flights. You want to estimate the probability that 15 or more flights out of 20 will be on - time at this airport. You simulate 20 flights 25 times and get the following numbers of on-time flights: What is your estimate of the probability? A) 0.16 B) 0.48 C) 0.52 D) 0.56 E) 13

C) roughly symmetric.

7. Below is a stemplot of the scores on a recent statistics test. (Key: 8|2 = 82%) The overall shape of this distribution is A) clearly skewed to the right. B) clearly skewed to the left. C) roughly symmetric. D) without a clear shape

A) roughly symmetric with no outliers.

8. Below is a histogram of the number of repetitions of a chin - up exercise the members of two high school gym classes could do. For reference: the minimum done was two students doing none; the most, two students doing 12. The overall shape of this distribution is A) roughly symmetric with no outliers. B) roughly symmetric with one outlier. C) clearly skewed left. D) clearly skewed right.

C) 17. 11 14 15 16 *17* 17 18 19 21

9. During the semester, all the students in a statistics class kept track of the number of mailings they received from a predatory payday lender. The count for each is displayed below: The median number of mailings for these students is: A) 15. B) 16. C) 17. D) 17.5. E) 18.

25. The correlation between the foot lengths of fathers and their (adult) sons, measured in inches, is r = 0.92. This tells us that: A) fathers with small feet tend to have sons with small feet. B) fathers with small feet tend to have sons with large feet. C) sons have, on the average, feet that are 0.92 times the length of their father's. D) 92 percent of all sons have feet that are bigger than their father's. E) there is almost no connection between the foot lengths of fathers and sons.

A) fathers with small feet tend to have sons with small feet.

38. A _____________ of an outcome is a number between 0 and 1 that expresses an individual's judgment of how likely the outcome is. A) personal probability B) expected value C) correlation D) randomness E) possibility

A) personal probability

15. Suppose that the Blood Alcohol Content (BAC) of students who drink five beers varies from student to student according to a Normal distribution with mean 0.07 and standard deviation 0.01. The middle 95% of students who drink five beers have a BAC between: A) 0.06 and 0.08. B) 0.05 and 0.09. C) 0.04 and 0.10. D) 0.03 and 0.11.

B) 0.05 and 0.09. Normal Distriubiton 95% = 2 Standard Deviations 1 Standard Deviation = 0.01 0.01 + 0.01 = 0.02 0.07 - 0.02 = 0.05 0.07 + 0.02 = 0.09

4. According to the FBI Uniform Crime Report, the robbery rate in the United States is 202 per 100,000 people. At that rate, how many robberies would there be in a state the size of Indiana (5.8 million people)? A) About 1200 B) About 12,000 C) About 120,000 D) About 1,200,000 E) Impossible to Say

B) About 12,000 202 / 100,000 = .00202 120,000/ 5,800,000 = .00202

29. A study of 6,600 men found that those who consumed a moderate amount of alcohol (one drink or less per night) have lower mortality (on the average) than those who drink none. Is this good evidence that drinking a moderate amount causes lower mortality? A) Yes, because the study is an experiment. B) No, because people who drink a moderate amount may differ from nondrinkers in other ways, such as income and exercise, that affect mortality. C) Yes, because the sample is so large that the margin of error will be quite small. D) No, because we can't generalize from 6,600 pe ople to the millions of adults in the country.

B) No, because people who drink a moderate amount may differ from nondrinkers in other ways, such as income and exercise, that affect mortality.

34. The probability of an outcome of a random phenomenon is: A) either 0 or 1, depending on whether or not the phenomenon can actually occur. B) the proportion of a very long series of repetitions on which the outcome occurs. C) the mean plus or minus two standard deviations. D) another name for its expected value. E) the confidence level.

B) the proportion of a very long series of repetitions on which t he outcome occurs.

33. If I toss a fair coin 5000 times: A) the number of heads will be close to 2500. B) the proportion of heads will be close to 0.5. C) the proportion of heads in these tosses is a parameter. D) the proportion of heads will be close to 50.

B) the proportion of heads will be close to 0.5.

3. The average wage of production workers (adjusted for the effects of inflation) was $11.08 an hour in 1981 and $10.35 an hour in 1991. In the decade of the 1980s, wages went down by about A) 73%. B) 7.3%. C) 7.0%. D) 6.6%

B.) 7.3%. (new - starting value) / starting value (10.35 - 11.08) / 11.08 (1991 - 1981) / 1981

6. In order to create a good graph, you must do each of the following EXCEPT A) clearly label the axes or provide a legend. B) use three - dimensional effects, many colors, and eye - catching backgrounds. C) avoid pictograms. D) make the data stand out.

B.) use three - dimensional effects, many colors, and eye - catching backgrounds.

37. Suppose you have five friends: Malik, Samson, Quint, Jennifer, and Monique.You randomly choose one of them to attend a basketball game with you. What is the probability that you choose Quint? A) 0.5 (either he is chosen or he isn't). B) 5 C) 0.2 D) 0 E) 1

C) 0.2

35. A Home Depot store receives a shipment of 500 cordless screwdrivers of the same model. The 500 boxes are labeled 0, 1, 2, 3, ... , 499. The inventory specialist at the store wishes to test five of the screwdrivers. She uses the table of random digits to choose a single pair of digits at random from all the possible pairs 00, 01, ... , 99. It happens that she chooses the pair 69. She then inspects all the phones whose labels end in the chosen pair of digits. In this case, she will inspect the phones with labels 69, 169, 269, 369, and 469. The chance that the phone labeled 341 would be one of those chosen was: A) 1 in 500 (or 1/500). B) 5 in 100 (or 5/100). C) 1 in 100 (or 1/100). D) 1 in 5 (or 1/5).

C) 1 in 100 (or 1/100). 5 screwdrivers out of 500 5 / 500 = 1 / 100

23. A correlation cannot have the value A) 0.4. B) -0.75. C) 1.5. D) 0.0. E) 0.99.

C) 1.5. Correlation (r) must be from -1 to 1.

49. Suppose you roll three fair six - sided dice. What is the probability of each die showing an even number (i.e., you roll no odd numbers)? A) 1/3 B) 1/6 C) 1/8 D) 1/2 E) 0

C) 1/8 1/2 x 1/2 x 1/2 = 1/8

13. Here are the number of text messages that each of a group of students sent during a recent statistics class: 12 14 0 12 11 14 11 15 15 14 What is the third quartile of the number of text messages? A) 11 B) 12 C) 14 D) 15 E) 118.0

C) 14 *0* / 11 *11* 12 /*12 14*/ 14 *14* 15 / *15* *Min / Q1/ M/ Q3 / Max*

18. The weight losses for participants in a large exercise and diet study vary according to a Normal distribution with mean 14.5 pounds and standard deviation 3 pounds. Approximately what percent of the participants lose less than 14.5 pounds? A) 16 percent B) 34 percent C) 50 percent D) 84 percent E) 95 percent

C) 50 percent Normal Distribution Mean = Median Mean of 14.5 Pounds = Median 14.5 Pounds Median = Midpoint of Data

32. A high correlation between two variables does not always mean that changes in one cause changes in the other. The best way to get good evidence that cause - and - effect is present is to A) select a simple random sample from the population of interest. B) arrange the data in a two- way table. C) carry out a randomized comparative experiment. D) make a scatterplot and look for a strong association. E) make a histogram and look for outliers.

C) carry out a randomized comparative experiment.

20. A Normal distribution always A) is skewed to the right. B) is skewed to the left. C) is symmetric. D) has a mean of 0. E) has more than one peak

C) is symmetric.

19. The mean of any density curve is the A) point where the curvature of the curve changes. B) point at which the curve reaches its highest value. C) point at which the curve would balance if made of solid material. D) point with half the area under the curve to its left and half to its right.

C) point at which the curve would balance if made of solid material.

39. A _______________ for a random phenomenon describes all the possible outcomes and indicates how to assign probabilities to any collection of outcomes. A) standard deviation B) median C) probability model D) boxplot E) scatterplot

C) probability model

11. The standard deviation of the numbers 68,979,821 and 68,979,823 is A) very large. B) zero. C) the same as the standard deviation of 1 and 3. D) None of these answers are correct.

C) the same as the standard deviation of 1 and 3. 3 - 1 = 2 68,979,823 - 68,979,821 = 2

5. The age, weight, imbiber status (drinker or nondrinker), level of education (high school graduate or not,) and earned income of a simple random sample of 1,463 people is measured. The number of variables measured is: A) 1463 —the size of the sample. B) six — age, weight, imbiber status, level of education, income, and number of high school graduates. C) five — age, weight, imbiber status, level of education, and income. D) three — age, weight, and income. Imbiber status and level of education are not variables because they don't have units such as years or pounds.

C.) five — age, weight, imbiber status, level of education, and income.

50. Suppose you toss a fair coin and roll a fair six-sided die. What is the probability your actions result in tails on the coin and 3 on the die? A) 1/8 B) 2/3 C) 1/6 D) 1/12 E) 0

D) 1/12 1/2 x 1/6 = 1/12

17. The third quartile is also called the: A) 3rd percentile. B) 25th percentile. C) 50th percentile. D) 75th percentile.

D) 75th percentile.

36. Suppose you have a bag of 10 sandwiches from the deli: one bacon, lettuce, and tomato (BLT) one ham on rye; and eight bologna sandwiches. You pull out one sandwich and discover that you've pulled out the ham on rye. If you do not put the sandwich back into the bag, what is the probability that you pull out a bologna sandwich the next time you pull one out? A) 1/10 B) 1/9 C) 8/10 D) 8/9 E) 0

D) 8/9 Bag of 10 Sandwiches 1 BLT, 1 Ham on Rye, 8 Bologna Sandwiches Pull Out One Ham on Rye Do Not Replace It 10 - 1 = 9 Sandwiches Total 8 Bolognas Left Probability of 8/9

48. Bunches of bananas arriving from their supplier reach a grocer with probability 0.12 of being too ripe to sell. To simulate the event that a single bunch of bananas arriving at the grocery is too ripe to sell, the produce manager could use two digits from a random generator with the convention (choose the best answer): A) 00, 01, 02, ... , 09, 10, 11 ∅ too ripe 12, 13, 14, ... , 97, 98, 99 ∅ acceptable B) 01, 02, 03, ... , 10, 11, 12 ∅ too ripe 13, 14, 15, ... , 98, 99, 00 ∅ acceptable C) 00, 01, 02, ... , 85, 86, 87 ∅ too ripe 88, 89, 90, ... , 97, 98, 99 ∅ defective D) Any answer choice is correct. E) None of the answer choices is correct.

D) Any answer choice is correct.

12. If the mean of a list of numbers is 12.4, and the standard deviation is zero, you know that: A) you have made an arithmetic mistake. B) the median is 12.4. C) all the numbers in the list are 12.4. D) Both answers "the median is 12.4" and "all the numbers in the list are 12.4" are correct

D) Both answers "the median is 12.4" and "all the numbers in the list are 12.4" are correct

30. A report in a medical journal notes that the risk of developing Alzheimer's disease among subjects who (voluntarily) regularly took the anti- inflammatory drug ibuprofen (the active ingredient in Advil) was about half the risk among those who did not. Is this good evidence that ibuprofen is effective in preventing Alzheimer's disease? A) Yes, because the study was a randomized, comparative experiment. B) No, because the effect of ibuprofen is confounded with the placebo effect. C) Yes, because the results were published in a reputable professional journal. D) No, because this is an observational study. A clinical trial would be needed to confirm (or not confirm) the observed effect. E) Yes, because a 50% reduction can't happen just by chance.

D) No, because this is an observational study. A clinical trial would be needed to confirm (or not confirm) the observed effect.

16. A study of grades at a large university finds that the mean GPA for all undergraduates is 2.77. The distribution of grades is roughly normal. To make this description useful we must also know: A) the correlation. B) the median. C) the slope. D) the standard deviation.

D) the standard deviation.

31. Perfect correlation means all of the following except: A) r = -1 or r = +1. B) all points on the scatterplot lie on a straight line. C) all variation in one variable is explained by variation in the other variable. D) there is a causal relationship between the variables. E) each variable is a perfect predictor of the other.

D) there is a causal relationship between the variables.

46. A multiple choice exam offers four choices for each question. Jason just guesses the answers, so he has probability 1/4 of getting any one answer right. You want to simulate whether Jason's answers to 10 questions are right or wrong. One correct way to do this is A) one digit from the random digit table simulates one answer, with 4 = right and all other digits = wrong. Ten digits from the table simulate 10 answers. B) one digit from the random digit table simulates one answer, with 0 or 1 = right and all other digits = wrong. Ten digits from the table simulate 10 answers. C) one digit from the random digit table simulates one answ er, with odd = right and even = wrong. Ten digits from the table simulate 10 answers. D) two digits from the random digit table simulate one answer, with 00 to 24 = right and 25 to 99 = wrong. Ten pairs of digits simulate 10 answers. E) two digits from the random digit table simulate one answer, with 00 to 04 = right and 05 to 99 = wrong. Ten pairs of digits simulate 10 answers.

D) two digits from the random digit table simulate one answer, with 00 to 24 = right and 25 to 99 = wrong. Ten pairs of digits simulate 10 answers.

2. A local police department gives all job applicants a test in American history. However, experience shows that these test scores are unrelated to future job performance. As a measure of ability to do police work, the history test scores: A) are response variables. B) are biased. C) are confounded. D) are invalid. E) have predictive validity.

D.) are invalid

24. In a scatterplot we can see A) a display of the five - number summary. B) whether or not we have a simple random sample. C) the shape, center, and spread of the distribution of a quantitative variable. D) the form, direction, and strength of a relationship between two quantitative variables.

D.) the form, direction, and strength of a relationship between two quantitative variables.

43. A game involving a pair of dice pays you $4 with probability 16/36, costs you $2 with probability 14/36, and costs you $6 with probability 6/36. What is your approximate probability of losing money in one play of the game? A) 0 B) 0.167 C) 0.444 D) 0.500 E) 0.556

E) 0.556 Costs you $2 = 14/36 Costs you $6 = 6/36 14/36 + 6/36 = 20/36 20/36 = 0.556

47. China has 1.36 billion people. Soft drink manufacturers work constantly to try to carve out a portion of that huge market. A Euromonitor study in 2014 showed that Coca - Cola held 63% of the entire Chinese soft drink market. A researcher wants to simulate choosing 10 Chinese soft - drink consumers at random and asking each if he or she purchases Coca- Cola. Use the correct assignment of digits from the previous question and the random digits below to simulate the answers of 10 Chinese citizens. Read across the row of random digits from left to right. How many of these 10 Chinese soft-drink consumers purchase Coca- Cola? 19223 95034 05756 28713 96409 12531 42544 82853

E) 8 Pick 10 Chinese Soft-Drink Consumers 63% of Consumers Drink Coke 00 - 62: Drink Coca-Cola 63 - 99: Do Not Drink Coca-Cola Ask Ten Chinese Citizens 19223 95034 05756 28713 96409 12531 42544 82853 1. 19 - Drink 2. 22 - Drink 3. 39 - Drink 4. 50 - Drink 5. 34 - Drink 6. 05 - Drink 7. 75 - Do Not Drink 8. 62 - Drink 9. 87 - Do Not Drink 10. 13 - Drink Out of 10 Chinese Citizens, 8 Drink Coca-Cola.

28. A least-squares regression line is not just any line drawn through the points of a scatterplot. What is special about a least- squares regression line? A) It passes through all the points. B) It minimizes the squared values of the data. C) It has slope equal to the correlation between the two variables. D) It describes how a response variable y changes as an explanatory variable x takes different values. E) It minimizes the sum of the squared vertical distances of the data points from the line.

E.) It minimizes the sum of the squared vertical distances of the data points from the line.

1. A radio talk show invites listeners to call a telephone number to vote Yes or No on whether they support a bond issue for a new school. About 1500 people call in. Over 80 percent say No. As an estimate of community opinion, this result is: A) accurate to within ± 3 percent with 95 percent confidence. B) not trustworthy because of nonsampling errors. C) not valid because the sample size of 1500 is too small. D) unethical due to lack of informed consent. E) badly biased due to voluntary response.

E.) badly biased due to voluntary response.