AP STATS MIDTERM

Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then a. P(A or B) = 1.0. b. P(A and B) = 0.16. c. P(A and B) = 1.0. d. P(A or B) = 0.16. e. both A. and B. are true.

a

For the density curve shown below, which statement is true? a. The area under the curve between 0 and 1 is 1. b. The density curve is symmetric. c. The density curve is skewed right. d. The density curve is Normal. e. None of the above is correct.

a

A civil engineer is testing the reliability of traffic signal controllers produced by two different companies. He has 20 sets of controllers from each company, and he has been given clearance to install them at 40 different intersections in the city. He randomly assigns the controllers from company A to 20 intersections and the controllers from company B to the other intersections. The most important reason for this random assignment is that a. randomization is a good way to create two groups of 20 intersections that are as similar as possible, so that comparisons can be made between the two groups. b. randomization eliminates the impact of any confounding variables. c. randomization makes the analysis easier since the data can be collected and entered into the computer in any order. d. randomization ensures that the study is double-blind. e. randomization reduces the impact of outliers.

a

A random variable Y has the following distribution: The value of the constant C is: a. 0.10. b. 0.15. c. 0.20. d. 0.25. e. 0.75.

a

A randomly selected student is asked to respond Yes, No, or Maybe to the question "Do you intend to vote in the next presidential election?" The sample space is { Yes, No, Maybe }. Which of the following represents a legitimate assignment of probabilities for this sample space? a. 0.4, 0.4, 0.2 b. 0.4, 0.6, 0.4 c. 0.3, 0.3, 0.3 d. 0.5, 0.3, -0.2 e. 1/4, 1/4, 1/4

a

An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that a. when corn prices are above average, soybean prices also tend to be above average. b. there is almost no relation between corn prices and soybean prices. c. when corn prices are above average, soybean prices tend to be below average. d. when soybean prices go up by 1 dollar, corn prices go up by 70 cents. e. the economist is confused, because correlation makes no sense in this situation.

a

Control groups are used in experiments in order to: a. control the effects of outside variables on the outcome. b. control the subjects of a study to ensure that all participate equally. c. guarantee that someone other than the investigators, who have a vested interest in the outcome, controls how the experiment is conducted. d. achieve a proper and uniform level of randomization. e. reduce the variability in results.

a

In order for the random variable X to have a geometric distribution, which of the following conditions must X satisfy? I. P < 0.5 II. The number of trials is fixed. III. Trials are independent. IV. The probability of success has to be the same for each trial. V. All outcomes in the sample space are equally likely. a. III and IV b. II, III, IV, and V c. I and III d. I, III, and V e. II and III

a

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X > $400)? a. 0.2119 b. 0.2881 c. 0.5319 d. 0.7881 e. 0.8450

a

Let the random variable X represent the weight of male black bears before they begin hibernation. Research has shown that X is approximately Normally distributed with a mean of 250 pounds and a standard deviation of 50 pounds. What is P(X > 325 pounds)? a. 0.0668 b. 0.2514 c. 0.7486 d. 0.8531 e. 0.9332

a

Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (We will ignore the small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The probability that a randomly chosen death was due to diabetes is about a. 0.96. b. 0.107. c. 0.042. d. 0.038. e. 0.030.

a

Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility vehicles. In this study, a. gas mileage is a response variable, and you expect to find a negative association. b. gas mileage is a response variable, and you expect to find a positive association. c. gas mileage is an explanatory variable, and you expect to find a strong negative association. d. gas mileage is an explanatory variable, and you expect to find a strong positive association. e. gas mileage is an explanatory variable, and you expect to find very little association.

a

Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern? a. A straight line is not a good model for the data. b. The correlation must be 0. c. The correlation must be positive. d. Outliers must be present. e. The regression line might or might not be a good model for the data, depending on the extent of the curve.

a

The mean speed of vehicles in the "cars only" lanes of the New Jersey turnpike is 68 miles per hour. The mean speed of vehicles in the "any vehicle" lanes is 64 miles per hour. What must be true about the mean speed of all vehicles on the turnpike, assuming these are the only types of lanes? a. It could be any number between 64 and 68 miles per hour. b. It must be larger than the median speed. c. It must be larger than 66 miles per hour. d. It must be 66 miles per hours. e. We don't have enough information to draw any conclusion about the mean speed of all vehicles.

a

The probability that you will be ticketed for illegal parking on campus is about 1/3. During the last nine days, you have illegally parked every day and have NOT been ticketed (you lucky person!). Today, on the 10th day, you again decide to park illegally. Assuming the outcomes are independent from day to day, the probability that you will be caught is a. 1/3 b. 1/3 + (1/3)^9 c. 1/3 - (1/3)^9 d. 1/10 e. 9/10

a

The proportion of scores in a standard Normal distribution that are greater than 1.25 is closest to: a. .1056 b. .1151 c. .1600 d. .8849 e. .8944

a

Which of the following statements are true? I. The area under a Normal curve is always 1, regardless of the mean and standard deviation. II. The mean is always equal to the median for any Normal distribution. III. The interquartile range for any Normal curve extends from a. I and II b. I and III c. II and III d. I, II, and III e. None of the above gives the correct set of true statements.

a

Which of these variables is least likely to have a Normal distribution? a. Annual income for all 150 employees at a local high school b. Lengths of 50 newly hatched pythons c. Heights of 100 white pine trees in a forest d. Amount of soda in 60 cups filled by an automated machine at a fast-food restaurant e. Weights of 200 of the same candy bar in a shipment to a local supermarket

a

You draw two marbles at random from a jar that has 20 red marbles and 30 black marbles without replacement. What is the probability that both marbles are red? a. 0.1551 b. 0.1600 c. 0.2222 d. 0.4444 e. 0.8000

a

Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number of occupants of a randomly-selected car on his street. Which of the following could be his model? a. a b. b c. c d. d e. e

b

A copy machine dealer has data on the number of copy machines x at each of 89 customer locations and the number of service calls in a month y at each location. Summary calculations give = 8.4, = 2.1, = 14.2, = 3.8, and r = 0.86. What is the slope of the least-squares regression line of number of service calls on number of copiers? a. 0.86 b. 1.56 c. 0.48 d. 2.82 e. Can't tell from the information given

b

A die is loaded so that the number 6 comes up three times as often as any other number. What is the probability of rolling a 1 or a 6? a. 2/3 b. 1/2 c. 3/8 d. 1/3 e. 1/4

b

A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear in these 1996 additional tosses? a. 996 b. 998 c. 1000 d. 1002 e. 1996

b

A random variable X has a probability distribution as follows: Where k is a positive constant. The probability P(X 2.0) is equal to a. 0.90. b. 0.25. c. 0.65. d. 0.15. e. 1.00.

b

A recent survey asked 100 randomly selected adult Americans if they thought that women should be allowed to go into combat situations. Here are the results, classified by the gender of the subject: The probability of a "Yes" answer, given that the person was Female, is a. 0.08 b. 0.16 c. 0.20 d. 0.40 e. 0.42

b

A rock concert producer has scheduled an outdoor concert. If it is warm that day, she expects to make a $20,000 profit. If it is cool that day, she expects to make a $5000 profit. If it is very cold that day, she expects to suffer a $12,000 loss. Based upon historical records, the weather office has estimated the chances of a warm day to be 0.60; the chances of a cool day to be 0.25. What is the producer's expected profit? a. $5,000 b. $11,450 c. $13,000 d. $13,250 e. $15,050

b

A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is = 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements is not necessarily true? a. For each one-point increase in performance rating, the raise will increase on average by $2000. b. The actual relationship between salary raises and performance rating is linear. c. A rating of 0 will yield a predicted raise of $1400. d. The correlation between salary raise and performance rating is positive. e. If the average performance rating is 1.2, then the average raise is $3800.

b

A small company that prints custom t-shirts has 6 employees, one of whom is the owner and manager. Suppose the owner makes $120,000 per year and the other employees make between $40,000 and $50,000 per year. One day, the owner decides to give himself a $30,000 raise. Which of the following describes how the company's mean and median salaries would change? a. The mean and median would both increase by $5,000. b. The mean would increase by $5,000 and the median would not change. c. The mean would increase by $6,000 and the median would not change. d. The median would increase by $6,000 and the mean would not change. e. The mean would increase by $6,000, but we cannot determine the change in the median without more information.

b

Eighty volunteers who currently use a certain brand of over-the-counter allergy medication have been recruited to participate in a trial of a new allergy medication. The volunteers are randomly assigned to one of two groups. One group continues to take their current medication, the other group switches to the new experimental medication. Each is asked after two weeks if their allergy symptoms are worse, better, or about the same as they were at the start of the study. Which of the follow best describes a conclusion that can be drawn from this study? a. We can determine whether the new drug reduces symptoms more than the old drug for anyone who suffers from allergies. b. We can determine whether the new drug reduces symptoms more than the old drug for the subjects in the study. c. We can determine whether the allergies sufferers' symptoms improved more with the new drug than with the old drug, but we can't establish cause and effect. d. We cannot draw any conclusions, since the all the volunteers were already taking the old drug when the experiment started. e. We cannot draw any conclusions, because there was no control group.

b

For the distribution of cookie bags described in Question 3, approximately what percent of the bags will likely be underweight (that is, less than 16 ounces)? a. 10 b. 16 c. 32 d. 64 e. None of the above

b

Here are the IQ test scores of 10 randomly chosen fifth-grade students: To make a stemplot of these scores, you would use as stems a. 0 and 1. b. 09, 10, 11, 12, 13, and 14. c. 96, 110, 118, 122, 125, 126, 130, 139, and 145. d. 0, 2, 3, 5, 6, 8, 9. e. None of the above is a correct answer.

b

In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below. The expected value of C is a. $155. b. $595. c. $875. d. $645. e. $495.

b

In the course described in #2, Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual? a. -2.0 b. 2.0 c. 3.0 d. 93 e. None of these

b

Jun and Deron are applying for summer jobs at a local restaurant. After interviewing them, the restaurant owner says, "The probability that I hire Jun is 0.7, and the probability that I hire Deron is 0.4. The probability that I hire at least one of you is 0.9." What is the probability that both Jun and Deron get hired? a. 0.1 b. 0.2 c. 0.28 d. 0.3 e. 1.1

b

Kitchen appliances don't last forever. The lifespan of all microwave ovens sold in the United States is approximately Normally distributed with a mean of 9 years and a standard deviation of 2.5 years. What percentage of the ovens last more than 10 years? a. 11.5% b. 34.5% c. 65.5% d. 69% e. 84.5%

b

Loretta is 20 months old and is 80 centimeters tall. What is her residual? a. 2.47 b. 2.47 c. -12.60 d. 12.60 e. 77.53

b

Mr. Yates picked up a dozen items in the grocery store with a mean cost of $3.25. Then he added an apple pie for $6.50. The new mean for all 13 items is a. $3.00 b. $3.50 c. $3.75 d. $4.88 e. None of the above

b

On May 11, 50 randomly selected subjects had their systolic blood pressure (SBP) recorded twice—the first time at about 9:00 a.m. and the second time at about 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect the correlation to be: a. near zero, as morning and afternoon readings should be independent. b. high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon. c. high and negative, as those with relatively high readings in the morning will tend to have relatively low readings in the afternoon. d. near zero, as correlation measures the strength of the linear association. e. near zero, as blood pressure readings should follow approximately a Normal distribution.

b

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The least-squares regression line is the line that a. minimizes the sum of the distances between the actual UV values and the predicted UV values. b. minimizes the sum of the squared residuals between the actual yield and the predicted yield. c. minimizes the sum of the distances between the actual yield and the predicted UV. d. minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values. e. minimizes the perpendicular distance between the regression line and each data point.

b

Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by: a. (10 3) * (1/8)^3*(7/8)^5 b. (10 3) * (1/8)^3*(7/8)^7 c. (8 3) * (1/8)^3*(7/8)^5 d. (8 3) * (1/8)^3*(7/8)^7 e. (10 3) * (7/8)^3*(1/8)^7

b

The Texas experiment described in the previous question a. has one factor: the type of AP Statistics curriculum a student is assigned to. b. has two factors: the type of AP Statistics curriculum and the teacher a student is assigned to. c. has two factors: the standard curriculum and one with the hands-on approach. d. has three factors: the type of AP Statistics curriculum, the teacher, and the class a student is assigned to. e. has three factors: the standard curriculum, the hands-on approach, and the teacher a student is assigned to.

b

The density curve below takes the value 0.5 on the interval 0 = x = 2 and takes the value 0 everywhere else. What percent of the observations lie between 0.5 and 1.2? a. 25% b. 35% c. 50% d. 68% e. 70%

b

The distribution of the heights of students in a large class is roughly Normal. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to: a. 2 b. 3 c. 6 d. 9 e. 12

b

The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range a. 65.5 inches to 70.5 inches b. 63 inches to 73 inches c. 60.5 inches to 75.5 inches d. 58 inches to 78 inches e. none of the above

b

The pie chart at right describes the distribution of favorite school subject for 300 high school students. Which of the following can we conclude from this graph? a. Math was the favorite subject for 26 students. b. English was the favorite subject of 96 students. c. Taken together, history, English, and the arts where the favorite subjects of less than half the students. d. No student said that Spanish was his or her favorite subject. e. Most of the English students were female.

b

The two-way table below gives information on seniors and juniors at a high school and by which means they typically get to school. You select one student from this group at random. What is the probability that this student typically takes a bus to school? a. 0.256 b. 0.309 c. 0.353 d. 0.455 e. 0.604

b

To test the effect of music on productivity, a group of assembly line workers are given portable mp3 players to play whatever music they choose while working for one month. For another month, they work without music. The order of the two treatments for each worker is determined randomly. This is a. an observational study. b. a matched pairs experiment. c. a completely randomized experiment. d. a block design, but not a matched pairs experiment. e. impossible to classify unless more details of the study are provided.

b

To test the effects of a new fertilizer, 100 plots were divided in half. Fertilizer A is randomly applied to one half, and B to the other. This is a. an observational study. b. a matched pairs experiment. c. a completely randomized experiment. d. a block design, but not a matched pairs experiment. e. impossible to classify unless more details of the study are provided.

b

We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose the households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random number table is Then the households selected are a. households 11 13 36 62 73 b. households 11 36 23 08 42 c. households 11 36 23 23 08 d. households 11 36 23 56 92 e. households 11 35 96 90 46

b

What electrical changes occur in muscles as they get tired? Student subjects are instructed to hold their arms above their shoulders as long as they can. Meanwhile, the electrical activity in their arm muscles is measured. This is a. an observational study. b. an uncontrolled experiment. c. a randomized comparative experiment. d. a matched pairs design. e. impossible to describe unless more details of the study are provided.

b

X and Y are independent random variables, and a and b are constants. Which one of the following statements is true? a. standard deviation (x+y) = std(x) + std(y) b. Var(x-y) = Var(x) + Var(y) c. Var(a+bx)= bVar(x) d. standard deviation (x-y) = std(x) - std(y) e. Var(x+y)= sqrt(Var(x)^2+Var(y)^2)

b

You have data for many families on the parents' income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot, a. the explanatory variable is parents' income, and you expect to see a negative association. b. the explanatory variable is parents' income, and you expect to see a positive association. c. the explanatory variable is parents' income, and you expect to see very little association. d. the explanatory variable is years of education, and you expect to see a negative association. e. the explanatory variable is years of education, and you expect to see a positive association.

b

You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have a probability of 0.6 of winning. The probability that you win the next two matches is a. 0.16. b. 0.36. c. 0.4. d. 0.6. e. 1.2.

b

You select one student from this group at random. If the student says he is a junior, what is the probability that he walks to school? a. 0.073 b. 0.160 c. 0.455 d. 0.600 e. 0.833

b

You select one student from this group at random. Which of the following statement is true about the events "Typically walks to school" and "Junior?" a. The events are mutually exclusive and independent. b. The events are not mutually exclusive but they are independent. c. The events are mutually exclusive, but they are not independent. d. The events are not mutually exclusive, nor are they independent. e. The events are independent, but we do not have enough information to determine if they are mutually exclusive.

b

A Texas school district wants to compare the effectiveness of a standard AP Statistics curriculum and a new "hands-on" AP Statistics curriculum. Two experienced teachers, Mr. Pryor and Mr. Legacy, each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. The subjects in this experiment are a. Mr. Pryor and Mr. Legacy. b. the two AP Statistics curricula. c. the students in the four classes. d. all students taking AP Statistics in Texas. e. only one: AP Statistics.

c

A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a profit of $5000 with probability 9/20, to break even with probability 5/20, and to lose $5000 with probability 3/20. The expected profit in dollars is a. 1500. b. 0. c. 3000. d. 3250. e. -1500.

c

It has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause illness if improperly cooked. Chickens are delivered to grocery stores in crates of 24. Assume the chickens are independently selected for inclusion in the crate. The probability that a certain crate has more than 4 contaminated chickens is a. 0.0424 b. 0.0686 c. 0.8889 d. 0.9313 e. 0.9576

c

A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting? a. Y has a binomial distribution with n = 40 observations and probability of success p = 0.5. b. Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided the deck is shuffled well. c. Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected. d. Y has a geometric distribution with n = 40 observations and probability of success p = 0.5. e. Y has a geometric distribution with n = 52 observations and probability of success p = 0.5.

c

A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation of 11.9 minutes. Approximately what proportion of their response times is over 30 minutes? a. 0.03 b. 0.21 c. 0.25 d. 0.75 e. 0.79

c

A friend has placed a large number of plastic disks in a hat and invited you to select one at random. He informs you that they have numbers on them, and that one of the following is the probability model for the number on the disk you have chosen. Which one is it? a. a b. b c. c d. d e. e

c

A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model? a. A residual plot is not an appropriate means for evaluating a linear model. b. The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players. c. The curved pattern in the residual plot suggests that the linear model is not appropriate. d. There are not enough data points to draw any conclusions from the residual plot. e. The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.

c

A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of adult women in one of the countries. About what percent of Country A women weigh between 110 and 240 pounds? a. 50% b. 65% c. 75% d. 85% e. 95%

c

A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information you conclude a. that the remedy is effective for the treatment of headaches. b. nothing, because the sample size is too small. c. nothing, because there is no control group for comparison. d. that the new treatment is better than aspirin. e. that the remedy is not effective for the treatment of headaches.

c

A randomly chosen subject arrives for a study of exercise and fitness. Consider these statements. I. After 10 minutes on an exercise bicycle, you ask the subject to rate his or her effort on the Rate of Perceived Exertion (RPE) scale. RPE ranges in whole-number steps from 6 (no exertion at all) to 20 (maximum exertion). II. You measure VO2, the maximum volume of oxygen consumed per minute during exercise. VO2 is generally between 2.5 liters per minute and 6 liters per minute. III. You measure the maximum heart rate (beats per minute). The statement(s) that describe a discrete random variable are a. I. b. II. c. I, III. d. I, II, III. e. None of the statements describe a discrete random variable.

c

A researcher for a consumer products company is field testing a new formula for laundry detergent. He has contracted with 60 families, each with two children, who have agreed to test the product. He randomly assigns 30 families to the group that will use the new formula and 30 to the group that will use the company's current detergent formula. The most important reason for this random assignment is that a. randomization makes the analysis easier since the data can be collected and entered into the computer in any order. b. randomization eliminates the impact of any confounding variables. c. randomization is a good way to create two groups of 30 families that are as similar as possible, so that comparisons can be made between the two groups. d. randomization ensures that the study is double-blind. e. randomization reduces the impact of outliers.

c

A researcher observes that, on average, the number of divorces in cities with Major League Baseball teams is larger than in cities without Major League Baseball teams. The most plausible explanation for this observed association is that the a. presence of a Major League Baseball team causes the number of divorces to rise (perhaps husbands are spending too much time at the ballpark). b. high number of divorces is responsible for the presence of Major League Baseball teams (more single men means potentially more fans at the ballpark, making it attractive for an owner to relocate to such cities). c. association is due to the presence of a lurking variable (Major League teams tend to be in large cities with more people, hence a greater number of divorces). d. association makes no sense, since many married couples go to the ballpark together. e. observed association is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.

c

A researcher reports that the participants in his study lost a mean of 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct? a. Your friend must not have followed the diet correctly, since she did not lose weight. b. Since your friend did not lose weight, the report must not be correct. c. The report gives only the mean. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results. d. In order for the study to be correct, we must now add your friend's results to those of the study and recompute the new average. e. Your friend is an outlier.

c

A maple sugar manufacturer wants to estimate the average trunk diameter of Sugar Maples trees in a large forest. There are too many trees to list them all and take a SRS, so he divides the forest into several hundred 10 meter by 10 meter plots, selects 25 plots at random, and measures the diameter of every Sugar Maple in each one. This is an example of a a. multistage sample. b. stratified sample. c. simple random sample. d. cluster sample. e. convenience sample.

d

A sample of 250 high school students were asked, "If you had $1000 to contribute to one kind of charitable organization, which type of organization would you choose? Below is a two-way table of responses to this question and gender.Which of the following conclusions seems to be supported by the data? a. Most of the females who chose a health organization would have chosen an environmental organization as their second choice, had they been asked. b. There is no association between gender and choice of organization. c. The proportion of males who said they would contribute to an environmental organization was higher than the proportion of females who said they would contribute such an organization. d. None of the students surveyed said they would contribute to religious organizations. e. The marginal distribution of Organization is 140, 110.

c

A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that the maximum value in the distribution, which was erroneously recorded as 40, actually had a value of 50. If we make this correction to the data, then a. the mean remains the same, but the median is increased. b. the mean and median remain the same. c. the median remains the same, but the mean is increased. d. the mean and median are both increased. e. we do not know how the mean and median are affected without further calculations, but the variance is increased.

c

According to the 1990 census, those states with an above-average number of people X, who fail to complete high school tend to have an above average number of infant deaths, Y. In other words, there is a positive association between X and Y. The most plausible explanation for this is a. X causes Y. Programs to keep teens in school will help reduce the number of infant deaths. b. Y causes X. Programs that reduce infant deaths will ultimately reduce high school dropouts. c. Lurking variables are probably present. For example, states with large populations may have both larger numbers of people who don't complete high school and more infant deaths. d. Both of these variables are directly affected by the higher incidence of cancer in certain states. e. The association between X and Y is purely coincidental.

c

An airline that wants to assess customer satisfaction chooses a random sample of 10 of its flights during a single month and asks all of the passengers on those flights to fill out a survey. This is an example of a a. multistage sample. b. stratified sample. c. cluster sample. d. simple random sample. e. convenience sample.

c

An article in the student newspaper of a large university had the headline "A's swapped for evaluations?" The article included the following. According to a new study, teachers may be more inclined to give higher grades to students, hoping to gain favor with the university administrators who grant tenure. The study examined the average grade and teaching evaluation in a large number of courses in order to investigate the effects of grade inflation on evaluations. "I am concerned with student evaluations because instruction has become a popularity contest for some teachers," said Professor Smith, who recently completed the study. Results showed that higher grades directly corresponded to a more positive evaluation. Which of the following would be a valid conclusion to draw from the study? a. A teacher can improve his or her teaching evaluations by giving good grades. b. A good teacher, as measured by teaching evaluations, helps students learn better, resulting in higher grades. c. Teachers of courses in which the mean grade is above average apparently tend to have above-average teaching evaluations. d. Teaching evaluations should be conducted before grades are awarded. e. All of the above.

c

An experiment to measure the effect of giving growth hormones to girls affected by Turner's Syndrome was carried out recently in Vancouver. All 34 girls in the study were given the growth hormone and their heights were measured at the time the hormone was given and again one year later. No measurements were made on their final adult heights. Which of the following is not a problem with this experiment: a. There was no blinding. b. There was no control group. c. Nonresponse bias d. There was insufficient attention to the placebo effect. e. Because final heights were not measured, it is impossible to tell if the hormone affected final height or only accelerated growth and made no difference to final height.

c

Below is a cumulative relative frequency graph for the 48 racers who finished the grueling 50km cross-country ski race at the 2010 Vancouver Olympics. Approximately what proportion of the racers finished the race in more than 2.15 hours? a. 0.17 b. 0.40 c. 0.45 d. 0.50 e. 0.55

c

For the density curve shown in Question 33, which statement is true? a. The mean and median are equal. b. The mean is greater than the median. c. The mean is less than the median. d. The mean could be either greater than or less than the median. e. None of the above is correct.

c

For the density curve shown in Question 41, which statement is true? a. The mean is greater than the median. b. The mean is less than the median. c. The mean and median are equal. d. The mean could be either greater than or less than the median. e. None of the above is correct.

c

If A = result of a single roll of a six-sided die and B = result of a single roll of an 8-sided die, then (mean a) =3.5 (std a)= 1.71 (mean b )= 4.5 (std b)= 2.29. If D = the difference B - A, then which of the following is true? a. (mean d)= 1 (std)= 1.71 + 2.29 b. (mean d)= 1 (std)= 1.71 - 2.29 c. (mean d)= 1 (std)= sqrt((1.71)^2 + (2.29)^2) d. (mean d)= 1 (std)= sqrt((1.71)^2 - (2.29)^2) e. (mean d)= 1 (std)= sqrt(1.71 + 2.29)

c

If PA. = 0.24 and PB. = 0.52 and A and B are independent, what is P(A or B)? a. 0.1248 b. 0.28 c. 0.6352 d. 0.76 e. The answer cannot be determined from the information given.

c

If you buy one ticket in the Provincial Lottery, then the probability that you will win a prize is 0.11. Given the nature of lotteries, the probability of winning is independent from month to month. If you buy one ticket each month for five months, what is the probability that you will win at least one prize? a. 0.55 b. 0.50 c. 0.44 d. 0.45 e. 0.56

c

If your score on a test is at the 60th percentile, you know that your score lies a. below the first quartile. b. between the first quartile and the median. c. between the median and the third quartile. d. above the third quartile. e. There is not enough information to say where it lies relative to the quartiles.

c

In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines? a. 86% b. 93% c. 74% d. 55% e. Can't tell from the information given

c

Leonardo da Vinci, the renowned painter, speculated that an ideal human would have an armspan (distance from the outstretched fingertip of the left hand to the outstretched fingertip of the right hand) that was equal to his height. The following computer regression printout shows the results of a least-squares regression of armspan on height, both in inches, for a sample of 18 high school students. Which of the following statements is false? a. This least-squares regression model would make a prediction that is 1.64 inches higher than da Vinci projected for a 62-inch tall student. b. If one of the students in the sample had a height of 70.5 inches and an armspan of 68 inches, then the residual for this student would be -2.78 inches. c. The least-squares regression line has a steeper slope than the equation for da Vinci's relationship between armspan and height. d. For every one-inch increase in height, the regression model predicts about a 0.84-inch increase in armspan. e. For a student 66 inches tall, our model would predict an armspan of about 67 inches.

c

Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected week, Dan will make less than a. $144 b. $216 c. $255 d. $30 e. $360

c

Mr. Nerdly asked the students in his AP Statistics class to report their overall grade point averages and their SAT Math scores. The scatterplot below provides information about his students' data. The dark line is the least-squares regression line for the data, and its equation is . Which of the following statements about the circled point is false? a. This student has a grade point average of about 2.9 and an SAT Math score of about 690. b. If we used the least-squares line to predict this student's SAT Math score, we would make a prediction that is too low. c. This student's residual is negative. d. Removing this data point would cause the correlation coefficient to increase. e. Removing this student's data point would increase the slope of the least-squares line.

c

People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor? a. 0 b. 0.280 c. 0.526 d. 0.720 e. 1

c

Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. The percent of bags that will contain between 16.0 and 16.1 ounces is about a. 10 b. 16 c. 34 d. 68 e. None of the above is correct.

c

The Interquartile range for the distribution of 50 states in the previous question is: a. 11.7% to 13.5% b. 117% to 135% c. 1.8% d. 2.7% e. 18%

c

The area under the standard Normal curve corresponding to -0.3 < Z < 1.6 is a. 0.3273 b. 0.4713 c. 0.5631 d. 0.9542 e. none of the above

c

The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be a. much smaller than 0.52 b. slightly smaller than 0.52 c. unchanged: equal to 0.52 d. slightly larger than 0.52 e. much larger than 0.52

c

The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61? a. 26 b. 76 c. 95 d. 190 e. None of these

c

The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude that a. owners of other brands of trucks are less satisfied than the owners of these three brands. b. Chevrolet owners are substantially more satisfied than Ford or Toyota owners. c. there is very little difference in the satisfaction of owners for the three brands. d. Chevrolet probably sells more trucks than Ford or Toyota. e. a pie chart would have been a better choice for displaying these data.

c

The following is a histogram showing the actual frequency of the closing prices of a particular stock on the New York Stock Exchange over a 50-day period. The class that contains the third quartile is: a. 10-20 b. 20-30 c. 30-40 d. 40-50 e. 50-60

c

The graph below is a Normal probability plot for the amount of rainfall (in acre-feet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true? a. The distribution is Normal. b. The distribution is approximately Normal. c. The distribution is skewed left. d. The distribution has no potential outliers. e. The distribution is skewed right.

c

The mean age (at inauguration) of all U.S. Presidents is approximately Normally distributed with a mean of 54.6. Barack Obama was 47 when he was inaugurated, which is the 11th percentile of the distribution. Which of the following is closest to the standard deviation of presidents' ages? a. -9.20 b. -6.18 c. 6.18 d. 7.60 e. 9.20

c

The proportion of observations from a standard Normal distribution that take values larger than -0.75 is about a. 0.2266 b. 0.7704 c. 0.7734 d. 0.7764 e. 0.8023

c

The two-way table below gives information on the performers in the New York Philharmonic Orchestra, categorized by section (type of instrument) and gender. You select one musician from this group at random. What is the probability that this person plays a woodwind? a. 0.091 b. 0.136 c. 0.159 d. 0.182 e. 0.571

c

There are 10 red marbles and 8 green marbles in a jar. If you take three marbles from the jar (without replacement), the probability that they are all red is: a. 0.069 b. 0.088 c. 0.147 d. 0.444 e. 0.171

c

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the following distribution: What is the probability that a randomly chosen household has at least two personal computers? a. 0.19 b. 0.20 c. 0.29 d. 0.39 e. 0.61

d

There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by predicted height = 50.3 + 6.01(age) where height is measured in centimeters and age in years. Which of the following is not correct? a. The estimated slope is 6.01, which implies that female children between the ages off 5 and 18 increase in height by about 6 cm for each year they grow older. b. The estimated height of a female child who is 10 years old is about 110 cm. c. The estimated intercept is 50.3 cm. We can conclude from this that the typical height of female children at birth is 50.3 cm. d. The average height of female children when they are 5 years old is about 50% of the average height when they are 18 years old. e. My niece is about 8 years old and is about 115 cm tall. She is taller than average for girls her age.

c

Use the information in the previous problem (31). About what percentage of the men are over 70.5 inches tall? a. 2.5 b. 5 c. 16 d. 32 e. 68

c

We may conclude that a. events A and B are independent. b. events A and B are mutually exclusive. c. either A or B always occurs. d. events A and B are complementary. e. none of the above is correct.

c

We say that the design of a study is biased if which of the following is true? a. A racial or sexual preference is suspected. b. Random placebos have been used. c. Certain outcomes are systematically favored. d. The correlation is greater than 1 or less than -1. e. An observational study was used when an experiment would have been feasible.

c

When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (in parts per million) Which of the following statements can we be sure is true? a. The mean lead level in the water is about 10 ppm. b. The mean lead level in the water is about 9 ppm. c. The median lead level in the water is 7 ppm. d. The median lead level in the water is 8 ppm. e. Neither the mean nor the median can be computed because some values are unknown.

c

Which of the following is a method for improving the accuracy of a sample? a. Use no more than 3 or 4 words in any question. b. When possible, avoid the use of human interviewers, relying on computerized dialing instead. c. Use large sample sizes. d. Use smaller sample sizes. e. Ask only questions for which the responses are quantitative variables.

c

Which of the following is correct? a. If the UV value increases by 1 Dobson unit, the yield is expected to increase by 0.0463 kg. b. If the yield increases by 1 kg, the UV value is expected to decrease by 0.0463 Dobson units. c. If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg. d. The predicted yield is 4.3 kg when the UV value is 20 Dobson units. e. None of the above is correct.

c

Which of the following properties is true for all Normal density curves? I. They are symmetric. II. The curve reaches its peak at the mean. III. 95% percent of the area under the curve is within one standard deviation of the mean. a. I only b. II only c. I and II only d. I and III only e. All three statements are correct.

c

Which of the following random variables is geometric? a. The number of phone calls received in a one-hour period b. The number of times I have to roll a six-sided die to get two 5s. c. The number of digits I will read beginning at a randomly selected starting point in a table of random digits until I find a 7. d. The number of 7s in a row of 40 random digits. e. All four of the above are geometric random variables.

c

Which of the following statements is/are true? I. Correlation and regression require that there are clearly-identified explanatory and response variables. II. Scatterplots require that both variables be quantitative. III. Every least-squares regression line passes through a. I and II only b. I and III only c. II and III only d. I, II, and III e. None of the above

c

You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked her attitude toward the product. You think there may be large differences between women who are employed outside the home and those who are not. Because of these differences, you should use a. a completely randomized design. b. a categorical variable. c. a block design. d. a stratified design. e. a multistage sample.

c

. You select one musician from this group at random. Which of the following statement is true about the events "Plays a woodwind" and "Male?" a. The events are mutually exclusive and independent. b. The events are not mutually exclusive but they are independent. c. The events are mutually exclusive, but they are not independent. d. The events are not mutually exclusive, nor are they independent. e. The events are independent, but we do not have enough information to determine if they are mutually exclusive.

d

A factory makes silicon chips for use in computers. It is known that about 90% of the chips meet specifications. Every hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded. What is the approximate mean and standard deviation of the number of chips meeting specifications? a. = 1.62; = 1.414 b. = 1.62; = 1.265 c. = 16.2; = 1.62 d. = 16.2; = 1.273 e. = 16.2; = 4.025

d

A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she's been authorized to repave for this study. She decides to carry out a matched pairs experiment. Which of the following is the best way for her to carry out the randomization for this study? a. Use a table of random digits to divide the 40 roadways into 20 pairs and then, for each pair, flip a coin to decide which pavement to use on which member of the pair. b. Subjectively divide the 40 roadways into 20 pairs (making the roadways within each pair as different as possible) and then, for each pair, flip a coin to decide which pavement to use on which member of the pair. c. Use a table of random digits to divide the 40 roadways into two groups of twenty, and then use the table of random digits a second time to decide which pavement to use on which group. d. Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement. e. Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin once to decide which pavement is put on the first half-mile of all the roadways.

d

A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per 100 milligrams of fruit. Six fruit packs were randomly assigned to each of the three storage times. The treatment, experimental unit, and response are respectively: a. A specific storage time, amount of vitamin C, a fruit pack b. A fruit pack, amount of vitamin C, a specific storage time c. Random assignment, a fruit pack, amount of vitamin C d. A specific storage time, a fruit pack, amount of vitamin C e. A specific storage time, the nutritionist, amount of vitamin C

d

A recent survey by a large-circulation Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important universities are to the Canadian economy." The main problem with using these results to draw conclusions about the general public's perception is a. insufficient attention to the placebo effect. b. no control group. c. lack of random assignment. d. lack of random selection. e. response bias.

d

A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation. Which of the following conclusions seems to be supported by the data? a. Republicans outnumber both Democrats and "Other." b. The conditional distribution of party affiliation for males is 1100. c. The marginal distribution of party affiliation is 1000, 1000. d. There is an obvious association between gender and political party registration. e. It is unclear whether there is an association between gender and political party registration.

d

A sample of student opinion at a Big Ten university selects an SRS of 200 of the 30,000 undergraduate students and a separate SRS of 100 of the 5,000 graduate students. This kind of sample is called a a. simple random sample. b. simple random sample with blocking. c. multistage random sample. d. stratified random sample. e. random cluster sample.

d

A small company estimating its photocopying expenses finds that the mean number of copies made per day for the past 12 months is 258 copies per day with a standard deviation of 24 copies per day. Which of the following is a correct interpretation of standard deviation? a. The number of copies made per day was always between 234 and 282. b. About 95% of the time, the number of copies made per day was between 234 and 282. c. The difference between the mean number of copies made per day and the median number of copies made per day was 24. d. On average, the number of copies made each day was about 24 copies per day away from the mean, 258. e. 1.5 times the interquartile range of copies made per day is 24.

d

A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties X and O are represented by x's and o's, respectively, in the following scatterplot. Which of the following statements is true? a. Considering Variety X only, there is a positive correlation between sepal length and width. b. Considering Variety O only, the least-squares regression line for predicting sepal length from sepal width has a positive slope. c. Considering both varieties together, there is a negative correlation between sepal length and width. d. Considering each variety separately, there is a negative correlation between sepal length and width. e. Considering both varieties together, the least-squares regression line for predicting sepal length from sepal width has a negative slope.

d

A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). A least-squares line was fit to the data. Here is the residual plot from this least-squares fit. What does the residual plot tell you about the linear model? a. The residual plot confirms the linearity of the fuel economy data. b. The residual plot does not confirm nor rule out the linearity of the data. c. The residual plot suggests that the model may be linear, but more data points are needed to confirm this. d. The residual plot clearly indicates that the data isn't linear. e. A residual plot is not an appropriate means for evaluating a linear model.

d

A survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. For a random sample of graduates, three variables are to be recorded: sex, starting salary, and area of specialization. Which of the follow best describes a conclusion that can be drawn from this study? a. Whether being female causes graduates of this nursing school to have lower (or higher) starting salaries than males. b. Whether being female causes graduates in this sample to have lower (or higher) starting salaries than males. c. Whether choosing certain area of specialization causes females graduates of this nursing school to have lower (or higher) starting salaries than males. d. Whether there is an association between sex and starting salary among graduates of this nursing school. e. Whether there is an association between sex and starting salary at all nursing schools similar to this one.

d

Select a random integer from -100 to 100. Which of the following pairs of events are mutually exclusive (disjoint)? a. A: the number is odd; B: the number is 5 b. A: the number is even; B: the number is greater than 10 c. A: the number is less than 5; B: the number is negative. d. A: the number is above 50; B: the number is less than 20. e. A: the number is positive; B: the number is odd.

d

According to the U.S. Bureau of Labor Statistics, the monthly percentage change in the number of jobs in a certain state for the twelve months of 2007 had a mean of 0.08% and a standard deviation of 1.70%. From this information we can conclude that a. The largest monthly change was 1.78% b. The distribution of monthly changes is strongly skewed to the right. c. Most of the monthly changes were negative. d. The magnitude of the monthly deviations from the mean change averaged about 1.70%. e. A mistake has been made. It makes no sense for the standard deviation to be greater than the mean.

d

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. The conditional probability of A, given B a. is 1/2. b. is 3/10. c. is 1/5. d. is 1/6. e. cannot be determined from the information given.

d

Are jet skis (otherwise known as personal watercraft, or PWC) dangerous? An article in the August 1997 issue of the Journal of the American Medical Association reported on a survey that tracked emergency room visits at randomly selected hospitals nationwide. The study recorded data on the number of jet skis in use and the number of accidents related to their use for the years 1990-1995. Computer output and a residual plot from a linear regression of jet-ski related injuries versus jet skis in use (PWC) are shown below. Use Scenario 3-16. The circled point represents a year when the number of PWC in use was 240,000. The number of observed injuries in that year was closest to: a. 350 b. 1250 c. 1600 d. 2800 e. 7300

d

Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10% of the time when a person is telling the truth and 95% of the time when a person is lying. Suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent one-person crime. Then the probability of observing no positive readings if all suspects plead innocent and are telling the truth is a. 0.409. b. 0.735. c. 0.00001. d. 0.591. e. 0.99999.

d

For a certain experiment you have 8 subjects, of which 4 are female and 4 are male. The name of the subjects are listed below: There are to be two treatment groups, A and B. If a randomized block design is used, with the subjects blocked by their gender, which of the following is not a possible group of subjects for treatment group A? a. Atwater, Chu, King, Liu b. Bacon, Chu, Liu, Moore c. Atwater, Diaz, Liu, King d. Atwater, Bacon, Chu, Johnson e. Atwater, Bacon, Johnson, King

d

For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Joseph is 22.5 months old. What is his predicted height? a. 50.80 b. 64.96 c. 65.96 d. 79.11 e. 87.40

d

For the data in the previous problem (27), which measures of center and spread would be most appropriate to use? a. Mean and standard deviation b. Mean and interquartile range c. Mean and range d. Median and interquartile range e. Median and standard deviation

d

For the density curve shown, which statement is true? a. The density curve is Normal. b. The density curve is skewed right. c. The density curve is skewed left. d. The density curve is symmetric e. None of the above is correct.

d

If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the sale but also goodwill. From past experience, a music store finds that the mean number of CDs sold in a sale is 845, the standard deviation is 15, and a histogram of the demand is approximately Normal. The manager is willing to accept a 2.5% chance that a CD will be sold out. About how many CDs should the manager order for an upcoming sale? a. 1295 b. 1070 c. 935 d. 875 e. 860

d

If data set A of (x, y) data has correlation r = 0.65, and a second data set B has correlation r = -0.65, then a. the points in A fall closer to a linear pattern than the points in B. b. the points in B fall closer to a linear pattern than the points in A. c. A and B are similar in the extent to which they display a linear pattern. d. you can't tell which data set displays a stronger linear pattern without seeing the scatterplots. e. a mistake has been made—r cannot be negative.

d

In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was = 10 + 0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam? a. 85.5 b. 90 c. 95 d. 95.5 e. None of these

d

In some courses (but certainly not in an intro stats course!), students are graded on a "Normal curve." For example, students within ± 0.5 standard deviations of the mean receive a C; between 0.5 and 1.0 standard deviations above the mean receive a C+; between 1.0 and 1.5 standard deviations above the mean receive a B-; between 1.5 and 2.0 standard deviations above the mean receive a B, etc. The class average on an exam was 60 with a standard deviation of 10. The bounds for a B- grade and the percent of students who will receive a B- grade if the marks are actually Normally distributed are a. (65, 75), 24.17% b. (65, 75), 12.08% c. (70, 75), 18.38% d. (70, 75), 9.19% e. (70, 75), 6.68%

d

In the previous question, the mean finish time is 2.164 hours and the standard deviation is 0.85 hours. The distribution is skewed right. What are the mean, standard deviation, and shape of the distribution of z-scores of the same data? a. Mean = 2.164, Standard deviation = 0.85, skewed right b. Mean = 2.164, Standard deviation = 0.85, skewed left c. Mean = 2.164, Standard deviation = 0.85, approximately normal d. Mean = 0, Standard deviation = 1, skewed right e. Mean = 0, Standard deviation = 1, approximately normal

d

In your top dresser drawer are 6 blue socks and 10 grey socks, unpaired and mixed up. One dark morning you pull two socks from the drawer (without replacement, of course!). What is the probability that the two socks match? a. 0.075 b. 0.375 c. 0.450 d. 0.500 e. 0.550

d

Roll one 10-sided die 12 times. The probability of getting exactly 4 eights in those 12 rolls is given by a. (10 4) * (1/10)^4 * (9/10)^8 b. (10 4) * (1/10)^4 * (9/10)^6 c. (12 4) * (1/10)^4 * (9/10)^6 d. (12 4) * (1/10)^4 * (9/10)^8 e. (12 4) * (1/10)^8 * (9/10)^4

d

The bar graph shows the distribution of breeds for all the champions of the annual World Canine Disc Championships from 1975 to 2009. Which of the following statement can be made on the basis of this graph? a. Mixed breed dogs have won the championship about twice as often as Australian Shepherds. b. Most of the mixed breed dogs were at least half Border Collie. c. None of the champion dogs were Labrador Retrievers. d. The graph exaggerates the difference between the number of champions of each breed category. e. Border Collies are larger dogs than Australian Shepherds.

d

The cumulative relative frequency graph below shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. The interquartile range for this distribution is approximately: a. 0.18 to 0.85 centimeters b. 5 to 7 centimeters c. 5.5 to 6.7 centimeters d. 1.2 centimeters e. 2 centimeters

d

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is a. Normally distributed, with mean 30 and standard deviation 15. b. Skewed to the right, with mean 30 and standard deviation 15. c. Normally distributed, with mean 0 and standard deviation 1. d. Skewed to the right, with mean 0 and standard deviation 1. e. Skewed to the right, but the mean and standard deviation cannot be determined without more information.

d

The graph below shows how mothers of young children respond to the question, "How many times a week do you choose fast food as a dining option for your family?" What's wrong with this method of presenting information? a. This kind of data should always be presented in a pie chart. b. The vertical axis should be "number of responses," not "percentage of responses." c. The horizontal axis should be divided into more than three categories. d. Using proportionally-sized hamburgers exaggerates differences between responses. e. We don't know if the mothers who responded were thinking about dinner, or both lunch and dinner.

d

The mean and standard deviation of the number of contaminated chickens in a crate are a. = 7; = 2.24 b. = 7; = 2.68 c. = 7; = 5.04 d. = 7.2; = 2.24 e. = 7.2; = 5.04

d

The mean birth weight of infants born at a certain hospital in the month of April was 128 oz. with a standard deviation of 10.2 oz. Which of the following is a correct interpretation of standard deviation? a. All the infants born in April weighed between 117.8 oz. and 138.2 oz. b. About half the infants born in April weighed between 117.8 oz. and 138.2 oz. c. The difference between the mean weight and the median weight of infants born in April was 10.2 oz. d. The distance between the weight of each infant born in April and the mean weight was, on average, about 10.2 oz. e. The mean weight of infants born in subsequent months is likely to be within 10.2 oz. of the mean weight in April.

d

The pie chart describes the distribution of state tree types for the 50 states in the United States. The category "Other" include all trees that are the state tree for two or fewer states. Which of the following conclusions can we draw from this chart? a. Some states have not designated a "state tree." b. The cottonwood is the state tree for 12 states. c. Taken together, oak, pine, and maple are the state trees for more than half the states. d. There are 10 states that have designated a pine as their state tree. e. There is no state that has designated the Eastern Red Cedar as its state tree.

d

The plot shown below is a Normal probability for a set of test scores. Which statement is true for these data? a. The data are clearly Normally distributed. b. The data are approximately Normally distributed. c. The data are clearly skewed to the left. d. The data are clearly skewed to the right. e. There is insufficient information to determine the shape of the distribution.

d

The population of the United States is aging, though less rapidly than in other developed countries. At right is a stemplot of the percents of residents aged 65 and older in each of the 50 states, according to the 2000 census. There are two outliers: Alaska has the lowest percent of older residents, and Florida has the highest. What is the percent for Florida? a. 13.8% b. 57% c. 176% d. 17.6% e. 5.7%

d

The probability of any outcome of a random phenomenon is a. the precise degree of randomness present in the phenomenon. b. any number as long as it is greater than 0 and less than 1. c. either 0 or 1, depending on whether or not the phenomenon can actually occur or not. d. the proportion of times the outcome occurs in a very long series of repetitions. e. none of the above.

d

The probability that a randomly selected subject in the study is Male or answered "No" is: a. 0.18 b. 0.36 c. 0.68 d. 0.92 e. 1.10

d

The variance of sum of two random variables X and Y is a. X + Y. b. (X)2 + (Y)2. c. X + Y, but only if X and Y are independent. d. (X)2 + (Y)2, but only if X and Y are independent. e. None of these.

d

Which of the following is a true statement? a. The binomial setting requires that there are only two possible outcomes for each trial, while the geometric setting permits more than two outcomes. b. A geometric random variable takes on integer values from 0 to n. c. If X is a geometric random variable and the probability of success is 0.85, then the probability distribution of X will be skewed left, since 0.85 is closer to 1 than to 0. d. An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting. e. The distribution of every binomial random variable is skewed right.

d

Which of the following is not true about all Normal distributions? a. The mean and median are equal b. The points at which the curvature changes from "up" to "down" (the points of inflection) are one standard deviation away from the mean on either side. c. About 2.5% of the values the variable takes on are more than two standard deviations above the mean. d. About 68% of the values of the variable are more than one standard deviation away from the mean. e. Z-scores of all the values of the variable have a mean of 0 and a standard deviation of 1.

d

Which of the following is the best interpretation of expected value? (In the choices below, "Exp(C)" represents expected value you found in question 1). a. If the company insures 10 cars of this model, they know they will incur 10 Exp(C) in costs. b. The maximum cost to the company for insuring this car model is Exp(C) per car. c. The company must insure at least Exp(C) of these cars to make a profit. d. If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C). e. If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately Exp(C).

d

Which statements below about least-squares regression are correct? I. Switching the explanatory and response variables will not change the least-squares regression line. II. The slope of the line is very sensitive to outliers with large residuals. III. A value of r2 close to 1 does not guarantee that the relationship between the variables is linear. a. Only I is correct. b. Only II is correct. c. Only III is correct. d. Both II and III are correct. e. All three statements—I, II, and III—are correct.

d

You select one musician from this group at random. If the person is a male, what is the probability that he plays a woodwind? a. 0.091 b. 0.136 c. 0.159 d. 0.182 e. 0.571

d

A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be -1.08. On the basis of this you would tell the college that a. the entrance exam is a good predictor of success. b. the exam is a poor predictor of success. c. students who do best on this exam will be poor students. d. students at this school are underachieving. e. the college should hire a new statistician.

e

A regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat gave the following results: Predicted Calories = 97.1053 + 9.6525(Fat). Which of the following is false? a. It is estimated that for every additional gram of fat in the cereal, the number of calories increases by about 10. b. It is estimated that in cereals with no fat, the total amount of calories is about 97. c. If a cereal has 2 g of fat, then it is estimated that the total number of calories is about 116. d. The correlation between amount of fat and calories is positive. e. If one cereal has 140 calories and 5 g of fat. Its residual is about 5 calories.

e

A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and you turn cards over, one at a time, beginning with the top card. Let Y be the number of cards you turn over until you observe the first red card. The random variable Y has which of the following probability distributions? a. the Normal distribution with mean 5 b. the binomial distribution with p = 0.5 c. the geometric distribution with probability of success 0.5 d. the uniform distribution that takes value 1 on the interval from 0 to 1 e. none of the above

e

A survey was done in the town of Mechanicsville to estimate the proportion of cars that are red and made by companies based in Japan. A random sample of 25 cars from a student parking lot at Lee-Davis High School was taken. Which of the following statements is not correct? a. This sample may not be representative of the cars in Mechanicsville because mainly students park at Lee-Davis High School. b. If the particular parking space is vacant, we can simply select another parking space at random because it is unlikely that a space being vacant is related to the color or manufacturer of the car. c. It would an error to simply select the first 25 parking spaces in the lot closest to the auditorium because there are a number of parking spaces there reserved for Drivers Ed vehicles, whose primary color is white. d. A different team doing the sampling independently would obtain different answers for their sample proportions. e. The results will be the same regardless of the time of day that the sample is taken.

e

A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him $5.00 per day to maintain the machine and rent the space for it. What are the mean and standard deviation for Y = the profit he earns from this machine in a randomly-selected week? a. Mean = 31.25, Standard deviation -$3.25 b. Mean = 31.25, Standard deviation $1.25 c. Mean = 31.25, Standard deviation $1.75 d. Mean = 26.25, Standard deviation $1.25 e. Mean = 26.25, Standard deviation $1.75

e

All but one of the following statements contains an error. Which statement could be correct? a. There is a correlation of 0.54 between the position a football player plays and his weight. b. We found a correlation of r = -0.63 between gender and political party preference. c. The correlation between the distance travelled by a hiker and the time spent hiking is r = 0.9 meters per second. d. We found a high correlation between the height and age of children: r = 1.12. e. The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.

e

At the beginning of the school year, a high-school teacher asks every student in her classes to fill out a survey that asks for their age, gender, the number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college after high school. Which of the following best describes the variables that are being measured? a. four quantitative variables b. five quantitative variables c. two categorical variables and two quantitative variables d. two categorical variables and three quantitative variables e. three categorical variables and two quantitative variables

e

Below is a pie chart of how a randomly selected group of people described the cost of their heath insurance. Which of the following bar graphs is equivalent to the pie chart? (look at graph)

e

For the histogram below, what is the proper ordering of the mean and median? Note that the graph is NOT numerically precise—only the relative positions are important. a. I is the mean and II is the median. b. II is the median and III is the mean. c. I is the median and II is the mean. d. I is the mean and III is the median. e. II is the mean and III is the median.

e

If a distribution is skewed to the right, which of the following is true? a. The mean must be less than the median. b. The mean and median must be equal. c. The mean must be greater than the median. d. The mean is either equal to or less than the median, e. It's impossible to tell which of the above statements is true without seeing the data.

e

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is: a. = 1.6; = 1.414 b. = 1.6; = 1.265 c. = 2; = 1.6 d. = 2; = 1.414 e. = 2; = 1.265

e

In the town of Tower Hill, the number of cell phones in a household is a random variable W with the following distribution: The probability that a randomly-selected household has at least two cell phones is a. 0.20. b. 0.25. c. 0.55. d. 0.70. e. 0.80.

e

Rainwater was collected in water collectors at 30 different sites near an industrial complex and the amount of acidity (pH level) was measured. The data ranged from pH 2.6 to pH 6.3. The following stem plot of the data was constructed. (Look at Graph)

e

The 16th percentile of a Normally distributed variable has a value of 25 and the 97.5th percentile has a value of 40. Which of the following is the best estimate of the mean and standard deviation of the variable? a. Mean 32.5; Standard deviation 2.5 b. Mean 32.5; Standard deviation 5 c. Mean 32.5; Standard deviation 10 d. Mean 30; Standard deviation 2.5 e. Mean 30; Standard deviation 5

e

The Hemlock Woolly Adelgid is an insect that has accidentally been released in Eastern U.S. forests from Asia. Since it has no natural enemies in the U.S., it is spreading rapidly. A forester studying the abundance of the insect in southern Vermont wants to determine if it has spread that far north. He randomly selects 200 hemlock trees in a large Vermont forest and finds that 46 of them show signs of damage from this insect. It would be appropriate to generalize the results of the study to a. all hemlock trees in southern Vermont. b. all trees in southern Vermont. c. the 200 hemlock trees that were randomly selected d. all hemlock trees in the United states. e. all hemlock trees in the forest from which the 200 trees were selected.

e

The following numbers appear in a table of random digits: A scientist will be measuring the total amount of leaf litter in a random sample (n = 5) of forest sites selected without replacement from a population of 45 sites. The sites are labeled 01, 02, . . . , 45 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following is correct? a. Her sample is 38, 25, 02, 38, 22 b. Her sample is 38, 68, 35, 02, 22 c. Her sample is 38, 35, 27, 28, 08 d. Her sample is 38, 65, 35, 02, 79 e. Her sample is 38, 35, 02, 22, 40

e

The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room is a. 40 years. b. 30 years. c. 25 years. d. less than 30 years. e. Cannot be determined from the information given.

e

The security system in a house has two units that set off an alarm when motion is detected. Neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. Suppose that for motion in a certain location, the probability that detector A goes off and detector B does not go off is 0.25, and the probability that A does not go off is 0.35. What is the probability that B goes off? a. 0.1. b. 0.35. c. 0.4. d. 0.65 e. 0.75.

e

The weights of the male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct? a. About 50% of the male students have weights between 150 and 185 pounds. b. About 25% of female students have weights above 130 pounds. c. The median weight of male students is about 162 pounds. d. The mean weight of female students is about 120 pounds. e. The male students have less variability than the female students.

e

Which of the following best describes what s = 1218.65 represents in this setting? a. The standard deviation of the observed values of the response variable, injuries. b. The standard deviation of the predicted values of the response variable, injuries. c. The standard deviation of the observed values of the explanatory variable, PWC's in use. d. The average of the products of each standardized value for PWC and the corresponding standardized value for injuries. e. The standard deviation of the residuals.

e

Which of the following statements is false? a. Nonresponse can cause bias in surveys because nonrespondents often tend to behave differently than people who respond. b. Non-sampling errors can distort the results of a census. c. Slight changes in the wording of questions can make a measurable difference in survey results. d. People will sometimes answer a question differently for different interviewers. e. Sophisticated statistical methods can always correct the results if the population you are sampling from is different from the population of interest, for example, due to undercoverage.

e

You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. "Least-squares" refers to a. Minimizing the sum of the squares of the 25 houses' heating costs. b. Minimizing the sum of the squares of the number of rooms in each of the 25 houses. c. Minimizing the sum of the products of each house's actual heating costs and the predicted heating cost based on the regression equation. d. Minimizing the sum of the squares of the difference between each house's heating costs and number of rooms. e. Minimizing the sum of the squares of the residuals.

e