AP stats study guide

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. b. c. d. e.

A.

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 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

A. 85.5

Control groups are used in experiments in order to accomplish which one of the following? a. Limit the effects of variables other than the explanatory variable 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 variability in results

A. Limit the effects of variables other than the explanatory variable on the outcome.

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. P(A or B) = 1.0.

Other things being equal, larger automobile engines are less fuel-efficient. You are planning an experiment to study the effect of engine size (in liters) on the fuel efficiency (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. gas mileage is a response variable, and you expect to find a negative association

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. it could be any number between 64 and 68 miles per hour

13. For the density curve shown above, 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. the area under the curve between 0 and 1 is 1

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 stemplot of the data was constructed. Which of the following boxplots is a correct representation of the same distribution? a. b. c. d. e.

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. 0.160

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. 0.309

Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 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. 09, 10, 11, 12, 13, and 14

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. 2.0

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. 63 inches to 73 inches

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. The events are not mutually exclusive but they are independent.

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. a matched pairs experiment

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 11362 35692 96237 90842 46843 62719 64049 17823. 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. households 11 36 23 08 42

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. minimizes the sum of the squared residuals between the actual yield and the predicted yield.

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. the mean would increase by $5,000 and the, median would not change

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. b. c. d. e.

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. 0.25

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. 0.526

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. 0.5631

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. 0.6352

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

C. 16

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. Country A: 92, 110, 120, 160, 240 About what percent of Country A women weigh between 110 and 240 pounds? a. 50% b. 65% c. 75% d. 85% e. 95%

C. 75%

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. I and II only

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. Which of the following is the most plausible explanation for this observed association? a. The 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. The 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. The association is due to confounding (Major League teams tend to be in large cities with more people, hence a greater number of divorces). d. The association makes no sense, since many married couples go to the ballpark together. e. The association is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.

C. The association is due to confounding (Major League teams tend to be in large cities with more people, hence a greater number of divorces).

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. The curved pattern in the residual plot suggests that the linear model is not appropriate

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. if the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg.

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. nothing, because there is no control group for comparison.

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.

C. simple random sample.

For the density curve shown above, 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. the mean is less than the median

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.

C. the mean must be greater than the median

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. Organization Gender Education Environment Health International Aid Other Female 19 33 50 28 10 Male 23 29 28 17 13 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. the proportion who said they would contribute to an environmental organization was higher than the proportion of females who said they would contribute such an organization

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 much more satisfied than Ford or Toyota owners. c. There are only small differences 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. there are only small differences in the satisfaction of owners for the three brands

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. unchanged: equal to 0.52

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. 0.500

The cumulative relative frequency graph at right 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. 1.2 centimeters

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 simple random sample of 25 cars from a parking lot at Lee-Davis High School was taken. Which of the following statements is correct? a. Since this is a simple random sample, it should be representative of all the cars in Mechanicsville. b. If a simple random sample of 15 cars were taken, we would expect the same amount of variability in the proportion of red cars as we would with a sample of 25 cars. c. An alternative method for getting a representative sample would be to select the 25 cars closest to a specified location, such as the entrance to the gymnasium. d. A different team doing the sampling independently would probably obtain a slightly different answer for their sample proportion. e. The results would be the same regardless of the time of day that the sample is taken.

D. A different team doing the sampling independently would probably obtain a slightly different answer for their sample proportion.

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. 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, six fruit packs, amount of vitamin C

D. A specific storage time, a fruit pack, amount of vitamin C

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 in the x direction 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 are correct

D. Both II and III are correct

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 distance between the weight of each infant born in April and the mean weight was, on average, about 10.2 oz.

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 following 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 a 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.

D. Whether there is an association between sex and starting salary among graduates of this nursing school.

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.

D. randomization ensures that the study is double-blind.

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. skewed to the right, with mean 0 and standard deviation 1.

The pie chart below 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. there are 10 states that have designated a pine as their state tree

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

E. 0.030

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 must be true? a. For each one-point increase in performance rating, the raise will increase on average by $1400. b. The actual relationship between salary raises and performance rating is linear. c. The residuals for half the observations in the dataset will be positive. d. The correlation between salary raise and performance rating is negative. e. If the mean performance rating is 1.2, then the mean raise is $3800.

E. If the mean performance rating is 1.2, then the mean raise is $3800

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. The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r=0.53.

The graph at right 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.

E. the distribution is skewed right