AP STAT FINAL
Roll one 8-sided die 10 times. What is the probability of getting exactly 3 sevens in those 10 rolls? a. b. c. d. e.
b.
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X = the amount that you win. Which of the following is the expected value of X? a. $0 b. $1 c. $2 d. $4 e. $6
b. $1
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. 1/2
A sample of production records for an automobile manufacturer shows the following figures for production per shift. 705 700 690 705 What is the standard deviation of this sample?
b. 7.07
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.
A basketball player shoots 8 free throws during a game. The sample space for counting the number she makes is a. any number between 0 and 1. b. {0, 1, 2, 3, 4, 5, 6, 7, 8}. c. {1, 2, 3, 4, 5, 6, 7, 8}. d. all sequences of 8 hits or misses, like HMMHHHMH. e. {HMMMMMMM, MHMMMMMM, MMHMMMMM, MMMHMMMM, MMMMHMMM, MMMMMHMM, MMMMMMHM, MMMMMMMH}.
b. {0, 1, 2, 3, 4, 5, 6, 7, 8}.
The density curve for a continuous random variable X has which of the following properties? a. The probability of any event is the area under the density curve between the values of X that make up the event. b. The total area under the density curve for X must be exactly 1. c. for any constant a. d. The density curve lies completely on or above the horizontal axis. e. All of the above.
e. All of the above.
Simple random sampling a. reduces bias resulting from poorly worded questions. b. reduces bias resulting from undercoverage and nonresponse. c. reduces bias resulting from the behavior of the interviewer. d. reduces variability. e. None of the above.
e. None of the above.
Which of these statements about the table of random digits is true? a. Every row must have exactly the same number of 0's and 1's. b. In the entire table, there are exactly the same number of 0's and 1's. c. If you look at 100 consecutive pairs of digits anywhere in the table, exactly 1 pair is 00. d. All of these statements are true. e. None of these statements are true.
e. None of these statements are true.
A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be -1.08. Based upon 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. the college should hire a new statistician.
One hundred people work at Lagtime Internet Services. Suppose after a particularly successful year, the president of the company decided to double his own salary and not change anyone else's. Assuming the president makes more than anyone else, which of the following statements about changes in measures of center and spread is true? a. The mean and standard deviation will increase, but the median and interquartile range will stay the same. b. The mean and interquartile range will increase, but the median and standard deviation will stay the same. c. The mean, standard deviation, and interquartile range will increase, but the median will stay the same. d. The mean will increase, but the median, standard deviation, and interquartile range will stay the same. e. The mean, median, standard deviation, and interquartile range will all increase.
a. The mean and standard deviation will increase, but the median and interquartile range will stay the same.
In a study of the link between high blood pressure and cardiovascular disease, a group of white males aged 35 to 64 was followed for 5 years. At the beginning of the study, each man had his blood pressure measured and it was classified as either "low" systolic blood pressure (less than 140 mm Hg) or "high" blood pressure (140 mm Hg or higher). The following table gives the number of men in each blood pressure category and the number of deaths from cardiovascular disease during the 5-year period. Low Blood Pressure High Blood Pressure Deaths 10 50 Total 2000 3500 Based on these data, which of the following statements is correct? a. These data are consistent with the idea that there is a link between high blood pressure and death from cardiovascular disease. b. The mortality rate (proportion of deaths) for men with high blood pressure is 5 times that of men with low blood pressure. c. These data probably understate the link between high blood pressure and death from cardiovascular disease, because men will tend to understate their true blood pressure. d. Although there were more deaths in the high blood pressure group, this is expected, because there were 1500 more men in that group. e. All of the above.
a. These data are consistent with the idea that there is a link between high blood pressure and death from cardiovascular disease.
Which of the following is the most important reason for randomly assigning subjects to treatment groups in an experiment? a. To create groups that are as similar as possible b. To eliminate bias c. To create a double-blind design d. To reduce random variation e. To counteract the placebo effect
a. To create groups that are as similar as possible
A stratified random sample addresses the same issues as which of the following experimental designs? a. a block design b. a double-blind experiment c. an experiment with a placebo d. a completely randomized design e. a confounded, nonrandomized study
a. a block design
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 $5,000 profit. If it is very cold that day, she expects to suffer a $12,000 loss. Based upon historical records, the estimated the probability of a warm day is 0.60 and the probability of a cool day is 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. $11,450
A random variable X has a probability distribution as follows: where k is a positive constant. P(X < 2) = a. 0.90 b. 0.25 c. 0.65 d. 0.15 e. 1.
b. 0.25
There are 10 students in Mrs. Sollom's afternoon Statistics class. The maximum point total for the most recent quarter was 200 points. The point totals for the 10 students are given in the stemplot below. Key: 17 | 9 represents a point total for the quarter of 179 points What is the median point total for this class?
b. 130.5
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.
Carrie and Vicki are both enthusiastic players of a certain computer game. Over the past year, Carrie's mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Vicki's mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Carrie gets a score of 14,000, and Vicki gets a score of 16,000. Calculate their z-scores and determine who won the contest. a. Carrie's z = 1.07; Vicki's z = 1.11; Vicki wins the contest. b. Carrie's z = 1.07; Vicki's z = 0.90; Carrie wins the contest. c. Carrie's z = 0.94; Vicki's z = 1.11; Vicki wins the contest. d. Carrie's z = 0.94; Vicki's z = 0.90; Carrie wins the contest. e. Carrie's z = 0.81; Vicki's z = 0.99; Vicki wins the contest.
b. Carrie's z = 1.07; Vicki's z = 0.90; Carrie wins the contest.
The computer output shown below gives the least-squares regression line for calories and protein (in grams) in one cup of 11 varieties of dried beans. Which of the following statements is a correct interpretation of the slope of the regression line? a. For each 1-unit increase in the calorie content, the predicted protein content increases by 2.08 grams. b. For each 1-unit increase in the calorie content, the predicted protein content increases by 0.063 grams. c. For each 1-gram increase in the protein content, the predicted calorie content increases by 2.08 grams. d. For each 1-gram increase in the protein content, the predicted calorie content increases by 0.063 grams. e. For each 1-gram increase in the protein content, the predicted calorie content increases by 0.024 grams.
b. For each 1-unit increase in the calorie content, the predicted protein content increases by 0.063 grams.
The scatter plot below describes the relationship between heights of 36 students and the number of words they spelled correctly in a spelling bee. The closed circles represent first graders and the open circles represent fifth graders. Which of the following statements is supported by the information in the scatter plot? a. The tallest first grader is taller than six of the third graders. b. When the data for first and fifth grades is combined, there is a moderately strong positive relationship between height and how many words were spelled correctly. c. Within each of the two grades, there is a strong negative relationship between height and how many words were spelled correctly. d. The tallest first grader spelled more words correctly than five of the fifth graders. e. All of the fifth graders spelled more words correctly than any of the first graders.
b. When the data for first and fifth grades is combined, there is a moderately strong positive relationship between height and how many words were spelled correctly.
You are told that your score on an exam is at the 85th percentile of the distribution of scores. Which of the following is a correct interpretation of this information? a. Your score was lower than approximately 85% of the people who took this exam. b. Your score was higher than approximately 85% of the people who took this exam. c. You answered 85% of the questions correctly. d. If you took this test (or one like it) again, you would score as well as you did this time 85% of the time. e. 85% of the people who took this test earned the same score you did.
b. Your score was higher than approximately 85% of the people who took this exam.
Fifty randomly selected subjects had their systolic blood pressure (SBP) recorded twice, once at 9:00 a.m. and again at 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 a distribution that is approximately Normal.
b. high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon.
A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. 28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77 Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). The median salary for the employees working for the company will a. be unchanged. b. increase by $3,000. c. be multiplied by $3,000. d. increase by . e. increase by $150.
b. increase by $3,000.
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. minimizes the sum of the squared residuals between the actual yield and the predicted yield.
Which of the following is not a random variable? a. the heights of randomly selected buildings in New York City b. the suit of a card randomly selected from a 52-card deck c. the number of children in randomly selected households in the United States d. the amount of money won (or lost) by the next person to walk out of a casino in Las Vegas e. All of the above are random variables.
b. the suit of a card randomly selected from a 52-card deck
Twelve people who suffer from chronic fatigue syndrome volunteer to take part in an experiment to see if shark fin extract will increase one's energy level. Eight of the volunteers are men, and four are women. Half of the volunteers are to be given shark fin extract twice a day, and the other half are to be given a placebo twice a day. We wish to make sure that four men and two women are assigned to each of the treatments, so we decide to use a block design with the men forming one block and the women the other. A block design is appropriate in this experiment if a. we want to be able to compare effects on energy level in men and women. b. we believe men and women will respond differently to treatments. c. gender equity is an important legal consideration in this study. d. we want the conclusions to apply equally to men and women. e. all of the above.
b. we believe men and women will respond differently to treatments
Miss Lee selects two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is an appropriate sample space for the possible outcomes? a. {red, black} b. {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red." c. {(red, red), (red, black), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red." d. {0, 1, 2}. e. All of the above.
b. {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red."
If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color. Color Brown Red Yellow Green Orange Blue Probability 0.3 0.2 ? 0.1 0.1 0.1 What is the probability of drawing a yellow candy? a. 0 b. 0.1 c. 0.2 d. 0.3 e. This is impossible to determine from the information given.
c. 0.2
If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color. Color Brown Red Yellow Green Orange Blue Probability 0.3 0.2 ? 0.1 0.1 0.1 What is the probability that you draw either a brown or a green candy? a. 0.1 b. 0.3 c. 0.4 d. 0.6 e. 0.7
c. 0.4
Which of the following statements about standard deviation is true? a. Standard deviation measures the typical distance data points in a distribution are from the median. b. Regardless of what units the data are in, standard deviation has no units. c. Standard deviation is always a non-negative number. d. If the data is measured in hours, standard deviation would be measured in hours squared. e. Standard deviation is resistant to outliers.
c. Standard deviation is always a non-negative number.
The mean height of men in the United States is 69 inches and the standard deviation is 3 inches. For U.S. women, the mean is 64 inches and the standard deviation is 2.7 inches. The tallest women in the Women's National Basketball Association is Brittney Griner, who is 80 inches tall (6 feet 8 inches). The tallest current player in the Men's NBA is Hasheem Thabeet, who is 87 inches tall (7 feet 5 inches). Which player is taller relative to others of the same sex in the U.S.? a. Griner, because her z-score is greater. b. Griner, because her z-score is closer to 0. c. Thabeet, because his z-score is greater. d. Thabeet, because his z-score is closer to 0. e. We can't compare relative standing unless we know both populations are Normally distributed.
c. Thabeet, because his z-score is greater.
For the density curve shown below, 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.
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): 5, 7, 12, bdl, 10, 8, bdl, 20, 6 Which of the following statements must be 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. The median lead level in the water is 7 ppm.
A group of 125 pick-up truck owners were asked what brand truck they owned and whether it had four-wheel drive. The results are given in the two-way table below. Four wheel drive? Yes No Total Truck Brand Ford 28 17 45 Chevy 32 18 50 Dodge 20 10 30 Total 80 45 125 You randomly select one truck owner. Which one of the following is true about the events "Owner has a Chevy" and "Owner's truck has four-wheel drive"? a. These two events are mutually exclusive and independent. b. These two events are mutually exclusive, but not independent. c. These two events are not mutually exclusive, but they are independent. d. These two events are neither mutually exclusive nor independent. e. These two events are mutually exclusive, but we do not have enough information to determine if they are independent.
c. These two events are not mutually exclusive, but they are independent
You select 40 cards from a standard deck of 52 cards. Let Y = 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. 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.
Does caffeine improve exam performance? Suppose all students in the 8:30 section of a course are given a "treatment" (two cups of coffee) and all students in the 9:30 section are not permitted to have any caffeine before a mid-term exam. Unfortunately, any systematic difference between the two sections on the exam might be due to the fact that the 8:30 and 9:30 classes have different instructors. This is an example of a. the placebo effect. b. bias. c. confounding. d. an observational study. e. stratification.
c. confounding
the binomial expression (8 2) (1/3)^7 (2/3)^6 gives the probability of a. at least 2 successes in 8 trials if the probability of success in one trial is 1/3. b. at least 2 successes in 8 trials if the probability of success in one trial is 2/3. c. exactly 2 successes in 8 trials if the probability of success in one trial is 1/3. d. exactly 2 successes in 8 trials if the probability of success in one trial is 2/3. e. at least 6 successes in 8 trials if the probability of success in one trial is 2/3.
c. exactly 2 successes in 8 trials if the probability of success in one trial is 1/3.
X and Y are two categorical variables. The best way to determine if there is a relation between them is to a. construct parallel boxplots of the X and Y values. b. draw dotplots of the X and Y values. c. make a two-way table of the X and Y values. d. compare medians and interquartile ranges of the X and Y values. e. compare means and standard deviations of the X and Y values.
c. make a two-way table of the X and Y values
Jessica was studying starfish populations and collected starfish of the species Pisaster. She was interested in the distribution of sizes of starfish on a certain shoreline. One measure of size is "arm length." Below is a cumulative relative frequency distribution for the arm length, in centimeters, of 102 Pisaster individuals. The Pisaster arm length of a particular starfish is 18.20 cm. Is this starfish unusually large? a. yes, this star fish is approximately at the 10th percentile for Pisaster arm length. b. yes, this star fish is approximately at the 18.20th percentile for Pisaster arm length. c. yes, this star fish is approximately at the 90th percentile for Pisaster arm length. d. no, this star fish is approximately at the 10th percentile for Pisaster arm length. e. no, this star fish is approximately at the 18.20th percentile for Pisaster arm length.
c. yes, this star fish is approximately at the 90th percentile for Pisaster arm length.
Mrs. Bukovac compiled the following table to compare the hand dominance of 200 Cleveland Heights High School students and what methods they prefer using to communicate with their friends. Communication method Cell phone/text In person Online Total Hand dominance Left-handed 12 13 9 34 Right-handed 43 72 51 166 Total 55 85 60 200 Suppose one student is chosen randomly from this group of 200. If you know the person that has been randomly selected is left-handed, what is the probability that they prefer to communicate with friends in person? a. 0.065 b. 0.153 c. 0.17 d. 0.382 e. 0.53
d. 0.382
You want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. You assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to execute as many simulations as possible, what is your estimate of the probability? 19226 95034 05756 07118 a. 1/20 b. 1/10 c. 5/10 d. 6/10 e. 2/3
d. 6/10
A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is On a day when the temperature is 20F, the regression line predicts that gas used will be about a. 1724 cubic feet. b. 1383 cubic feet. c. 1325 cubic feet. d. 964 cubic feet. e. none of these.
d. 964 cubic feet.
For a certain experiment you have 8 subjects, of which 4 are female and 4 are male. The names of the subjects are listed below: Males: Atwater, Bacon, Chu, Diaz. Females: Rae, Moneypenny, Haney, Heart 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, Moneypenny, Haney b. Bacon, Chu, Haney, Heart c. Atwater, Diaz, Haney, Moneypenny d. Atwater, Bacon, Chu, Rae e. Atwater, Bacon, Rae, Moneypenny
d. Atwater, Bacon, Chu, Rae
A study of the effects of television on child development measured how many hours of television each of 125 grade school children watched per week during a school year and each child's reading score. Which variable would you put on the horizontal axis of a scatterplot of the data? a. reading score, because it is the response variable b. reading score, because it is the explanatory variable c. hours of television, because it is the response variable d. hours of television, because it is the explanatory variable e. it makes no difference, because there is no explanatory-response distinction in this study
d. hours of television, because it is the explanatory variable
An ecologist who was studying starfish populations collected starfish of the species Pisaster was interested in the distribution of sizes of starfish on a certain shoreline. One measure of size is "arm length." Below is a cumulative relative frequency distribution for the arm length, in centimeters, of 102 Pisaster individuals. The Pisaster arm length of a particular starfish is 15.20 cm. Is this starfish unusually large? a. yes, this star fish is approximately at the 50th percentile for Pisaster arm length. b. yes, this star fish is approximately at the 15.20th percentile for Pisaster arm length. c. yes, this star fish is approximately at the 90th percentile for Pisaster arm length. d. no, this star fish is approximately at the 50th percentile for Pisaster arm length. e. no, this star fish is approximately at the 15.20th percentile for Pisaster arm length.
d. no, this star fish is approximately at the 50th percentile for Pisaster arm length.
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 2011 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. the magnitude of the monthly deviations from the mean change averaged about 1.70%.
A basketball player makes 75% of his free throws. We want to estimate the probability that he makes 4 or more free throws out of 5 attempts (we assume the shots are independent). To do this, we use the digits 1, 2, and 3 to correspond to making the free throw and the digit 4 to correspond to missing the free throw. If the table of random digits begins with the digits below, how many free throws does he hit in our first simulation of five shots? 19223 95034 58301 a. 1 b. 2 c. 3 d. 4 e. 5
e. 5
The following numbers appear in a table of random digits: 38683 50279 38224 09844 13578 28251 12708 24684 Mrs. Singleton 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, and 22. b. Her sample is 38, 68, 35, 02, and 22. c. Her sample is 38, 35, 27, 28, and 08. d. Her sample is 38, 65, 35, 02, and 79. e. Her sample is 38, 35, 02, 22, and 40.
e. Her sample is 38, 35, 02, 22, and 40.
If the values in a data set are in feet, then what are the units for the standardized values? a. feet b. square feet c. square root of feet d. inches e. Standardized values do not have units.
e. Standardized values do not have units.
One characteristic of roller coasters that contributes to the maximum speed of the ride is the track's maximum height. Show below is computer output for a regression of maximum speed (in miles/hours) on maximum height (in feet) for nine roller coasters that opened recently around the world. Which of the following best describes what S = 10.537 represents in this setting? a. This represents the standard deviation of the observed values of the response variable, speed. b. This represents the standard deviation of the predicted values of the response variable, speed. c. This represents the standard deviation of the observed values of the explanatory variable, height. d. This represents the average of the products of each standardized value for height and the corresponding standardized value for speed. e. This represents the standard deviation of the residuals.
e. This represents the standard deviation of the residuals.
A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is When the temperature goes up 1 degree, what happens to the gas usage predicted by the regression line? a. It goes up 1 cubic foot. b. It goes down 1 cubic foot. c. It goes up 19 cubic feet. d. It goes down 19 cubic feet. e. It cannot be determined without seeing the data.
d. It goes down 19 cubic feet.
Among the students at a large university who describe themselves as vegetarians, some eat fish, some eat eggs, some eat both fish and eggs, and some eat neither fish nor eggs. Mrs. Knaggs chooses a vegetarian student at random. Let E = the event that the student eats eggs, and let F = the event that the student eats fish. Which of the following Venn diagrams has correctly shaded the event that the student eats neither fish nor eggs? a. b. c. d. e.
a.
Below is a two-way table summarizing the number of cylinders in selected car models manufactured in six different countries. Which of the following is a marginal distribution? a. The percentage of all four-cylinder cars manufactured in Germany. b. The number of four-cylinder cars manufactured in Germany. c. The percentage of all cars manufactured in each country. d. The percentage of cars manufactured in Germany for each number of cylinders. e. The number of cylinders: 4, 5, 6, 8.
c. The percentage of all cars manufactured in each country.
Select a random integer from -100 to 100. Which of the following pairs of events are mutually exclusive (mutually exclusive)? 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. A: the number is above 50; B: the number is less than 20
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 r 2 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. II and III are correct. e. I, II, and III are correct.
d. II and III are correct.
An ecologist who was studying starfish populations collected starfish of the species Pisaster was interested in the distribution of sizes of starfish on a certain shoreline. One measure of size is "arm length." Below is a cumulative relative frequency distribution for the arm length, in centimeters, of 102 Pisaster individuals. What are the approximate values of the median and interquartile range of this distribution? a. median = 15; interquartile range = 12 and 16 b. median = 13; interquartile range = 13 and 16 c. median = 13; interquartile range = 3 d. median = 13; interquartile range = 4 e. median = 15; interquartile range = 4
e. median = 15; interquartile range = 4
Which one of the following statements is correct? a. Small dogs bark more often than big dogs, so the correlation between dog size and barking frequency is positive. b. Women tend to be, on average, about 3.5 inches shorter than the men they marry, so the correlation between the heights of spouses must be negative. c. A researcher finds the correlation between the shoe size of children and their score on a reading test to be 0.22. The researcher must have made a mistake because these two variables are clearly unrelated and must have correlation 0. d. If people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive. e. The correlation r equals the proportion of times that two variables lie on a straight line.
d. If people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive.
Here are the exam scores for the 15 students in Mrs. Stevenson's statistics class: 72 75 75 78 81 81 85 89 90 90 90 91 95 95 98. Spencer was at the 80th percentile of the distribution. What score did Spencer earn on the exam? a. 75 b. 78 c. 81 d. 91 e. 95
e. 95
Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. Which of the following is the proportion of infants with birthweights under 95 oz.? a. 0.160 b. 0.025 c. 0.340 d. 0.500 e. 0.815
a. 0.160
Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random without replacement and note the two numbers observed. The sample space consists of the three equally likely outcomes (1, 2), (1, 3), and (2, 3). Let X = the sum of the numbers on two balls selected. Which of the following is the correct probability distribution for X? a. b. c. d. e.
b.
There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth five points and only one option per question is correct. Suppose the student guesses the answer to each question, and the guesses from question to question are independent. Which of the following expresses the probability that the student gets no questions correct? a. (0.25)^20 b. (0.75)^20 c. (20 1) (0.25)(0.75)^19 d. (5 1) (0.25)(0.75)^4 e. (5 1) (0.25)^4(0.75)
b. (0.75)^20
To test the effects of a new fertilizer, 100 plots were divided in half. Fertilizer A is randomly applied to one half of each plot, 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. a matched pairs experiment.
In a certain town, 60% of the households have fiber optic internet access, 30% have at least one high-definition television, and 20% have both. What percent of households have neither fiber optic internet or high-definition television? a. 0% b. 10% c. 30% d. 80% e. 90%
c. 30%
The area under the standard Normal curve corresponding to z > -1.22 is closest to what value? a. 0.1112 b. 0.1151 c. 0.4129 d. 0.8849 e. 0.8888
e. 0.8888
You can roughly locate the median of a density curve by eye because it is a. the point at which the curve would balance if made of solid material. b. the point that divides the area under the curve into two equal parts. c. the point at which the curve reaches its peak. d. the point where the curvature changes direction. e. the point at which the height of the graph is equal to 1.
b. the point that divides the area under the curve into two equal parts.
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. 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. either A or B always occurs.
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
Which of the following is true about every random variable? I. It takes on numerical or categorical values. II. It describes the results of a random phenomenon. III. Its behavior can be described by a probability distribution. a. I only b. II only c. III only d. II and III e. All three statements are true.
d. II and III
IQs among undergraduates at Mountain Tech are approximately Normally distributed. The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100 and 120. What is the approximate value of the standard deviation of these IQs? a. 5 b. 10 c. 15 d. 20 e. 25
a. 5
The two-way table below gives information on the performers in the New York Philharmonic Orchestra, categorized by section (type of instrument) and gender. Type of instrument Strings Woodwinds Brass Total Gender Male 24 8 12 44 Female 37 6 1 44 Total 61 14 13 88 You select one musician from this group at random. What is the probability that this person plays a woodwind?
c. 0.159
The standard deviation of 16 peoples' weights (in pounds) is computed to be 5.4. The units for the variance of these measurements is a. pounds. b. square root pounds. c. pounds squared. d. unitless. Variance never has units. e. ounces.
c. pounds squared.
The principle reason for replication in designing experiments is that it a. distinguishes a treatment effect from the effects of other, possibly confounding variables. b. allows double-blinding. c. reduces sampling variability. d. creates approximately equal groups for comparison. e. eliminates the placebo effect.
c. reduces sampling variability.
An office supply catalog gives a description of bookshelves that includes the following variables. Which of these variables is categorical? a. the width of a bookshelf in inches b. the width of a bookshelf in feet c. the color of the bookshelf d. the height of a bookshelf in inches e. the weight of a bookshelf
c. the color of the bookshelf
A farmer wishes to determine which of two brands of baby pig pellets, Kent or Moormans, produces better weight gains. Two of his sows each give birth to litters of 10 pigs on the same day, so he decides to give the baby pigs in litter A only Kent pellets, while the pigs in litter B will get only Moormans pellets. After four weeks, the average weight gain for pigs in litter A is greater than the average weight gain for pigs in litter B. The brand of pellets is a. a parameter. b. the response variable. c. the explanatory variable. d. the placebo effect. e. a dependent variable.
c. the explanatory variable
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. What is the probability of observing no positive readings if all suspects plead innocent and are telling the truth? a. 0.409 b. 0.735 c. 0.00001 d. 0.590 e. 0.99999
d. 0.590
Mr. Cottrell asked the 26 seniors in his statistics class how many AP® courses they had taken during high school. Below is a dotplot summarizing the results of his survey. What is the interquartile range for the number of AP® courses? a. 3 to 4 b. 2.5 to 5 c. 3 to 5 d. 2 e. 2.5
d. 2
Suppose that 40% of the cars in a certain town are white. A person stands at an intersection waiting for a white car. Let X = the number of cars that must drive by until a white one drives by. What is the expected value of X? a. 1 b. 1.5 c. 2 d. 2.5 e. 3
d. 2.5
A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. What is the mean number of customers that make a purchase during the first hour that the store is open? a. 2 b. 2.5 c. 2.9 d. 3 e. 4
d. 3
Mr. Eyabi wants to know, does caffeine improve exam performance? Suppose all students in the 8:30 section of a course are given a "treatment" (two cups of coffee) and all students in the 9:30 section are not permitted to have any caffeine before a mid-term exam. Suppose half of the 8:30 students are randomly allocated to the treatment group (two cups of coffee), the other half to the control group (two cups of decaf). In addition, half of the 9:30 students are randomly allocated to the treatment group, the other half to the control group. This is an example of a a. voluntary response study. b. stratified sampling procedure. c. matched pairs design. d. completely randomized design. e. randomized block design.
e. randomized block design.
A random sample of 1500 adults in Ohio were asked if they support an increase in the state sales tax from 5% to 6%. Let X = the number in the sample that say they support the increase. Suppose that 4% of all adults in Ohio support the increase. Which of the following is the approximate standard deviation of X? a. 0.04 b. 0.24 c. 7.59 d. 60 e. 9.20
c. 7.59
The mean number of days that the midge Chaoborus spends in its larval stage is 14.1 days, with a standard deviation of 2.2 days. This distribution is skewed toward higher values. What is the z-score for an individual midge that spends 12.7 days in its larval stage? a. -1.11 b. -0.64 c. 0.64 d. 0.94 e. None of these, because a z-score cannot be used unless the distribution is Normal.
b. -0.64
If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color. Color Brown Red Yellow Green Orange Blue Probability 0.3 0.2 ? 0.1 0.1 0.1 What is the probability that you do not draw a red candy? a. 0.2 b. 0.3 c. 0.7 d. 0.8 e. This is impossible to determine from the information given.
d. 0.8
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 one standard deviation below the mean to one standard deviation above the mean. 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. I and II
What is the principle purpose of control in a randomized comparative experiment? a. Eliminating bias b. Isolating the effect of the treatment variable by keeping all other variables the same in the treatment groups c. Creating treatment groups that are as similar as possible d. Reducing the impact of random variation arising from random assignment to groups e. Ensuring that an experiment is conducted in a double blind fashion
b. Isolating the effect of the treatment variable by keeping all other variables the same in the treatment groups
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 cannot determine how the mean and median are affected without further calculations, but the variance is increased.
c. the median remains the same, but the mean is increased.
The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 1997. What percent of the schools have an acceptance rate of under 20%? a. 3% b. 4% c. 12% d. 16% e. 24%
d. 16%
Below is a histogram of the heights of gold-medal-winning high jumps in the Olympic Games since 1896. Based on this histogram, what is the percentage of the winning jumps that were at least 80 inches? a. 10% b. 35% c. 45% d. 55% e. 90%
d. 55%
Forty pound bags of bird seed do not have exactly 40 pounds of seed, but the weight should be close to that. A sample of 25 bags of birdseed had a mean weight of 39.5 pounds and a standard deviation of 0.25 pounds. Which of the following is a correct interpretation of the standard deviation? a. All the bags of birdseed weighed between 39.25 and 39.75 pounds. b. About half the bags of birdseed weighed between 39.25 and 39.75 pounds. c. The difference between the mean weight and the median weight of the bags of birdseed was 0.25 pounds. d. The distance between the weight of each bag of birdseed and the mean weight was, on average, about 0.25 pounds. e. The mean weight of bags of birdseed that will be produced in future batches is likely to be within 0.25 pounds of the current mean weight.
d. The distance between the weight of each bag of birdseed and the mean weight was, on average, about 0.25 pounds.
When controlled experiments are impractical or unethical, which of the following would be necessary to establish a cause-and-effect relation between two variables? a. Strong association between the variables. b. An association between the variables is observed in many different settings. c. The alleged cause is plausible. d. There is no other obvious variable whose effect is confounded with the explanatory variable in the study. e. All of the above.
e. All of the above.
You catch 10 cockroaches in your bedroom and measure their lengths in centimeters. Which of these sets of numerical descriptions are all measured in centimeters? a. median length, variance of lengths, largest length b. median length, first and third quartiles of lengths c. mean length, standard deviation of lengths, median length d. mean length, median length, variance of lengths. e. both (b) and (c)
e. both (b) and (c)
There are 10 students in Mrs. Meizius's afternoon Statistics class. The maximum point total for the most recent quarter was 200 points. The point totals for the 10 students are given in the stemplot below. Key: 17 | 9 represents a point total for the quarter of 179 points Based upon the shape of the stemplot, we can conclude that a. the mean is greater than the median. b. the mean is less than the median. c. the standard deviation is greater than the range. d. the standard deviation is greater than the mean. e. the standard deviation is greater than the median.
a. the mean is greater than the median.
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. cannot determine from the information given
b. 1.56
A restaurant maître d' wants to be able to predict the time customers will have to wait for a table based upon how many names are on her waiting list. She collects data on y = the time a group of customers wait for a table, and x = the number of names already on the waiting list when that group is added to the list. She finds that the relationship is roughly linear, and calculates the least-squares regression line. One group waited 15 minutes when there were 4 names ahead of them on the list. Which expression below represents the residual for this observation? a. 4-[2.8+3.77(15)] b. 15-[2.8+3.77(4)] c. [2.8+3.77(4)]+15 d.[2.8+3.77(4)]-15 e.[2.8+3.77(4)]-4
b. 15-[2.8+3.77(4)]
Consider the following cumulative relative frequency graph of the scores of children who played the game Skeeball at a birthday party. Students who earn a score of at least 80 win 5 tickets. What percentage of children who played Skeeball won 5 tickets? a. 15% b. 20% c. 25% d. 30% e. 50%
b. 20%
Here are the exam scores for the 15 students in Mr. Kirk's statistics class: 72 75 75 78 81 81 85 89 90 90 90 91 95 95 98. Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam? a. 75 b. 78 c. 81 d. 91 e. 95
b. 78
Mr. Affie records the heights (in centimeters) of the male and female students in his class and summarizes the results in the following boxplots: Which of the following conclusions can be drawn from this graph? a. About 50% of the male students have heights between 170 and 178 centimeters. b. About 25% of the male students are taller than the tallest female student. c. The median height of male students is about 163 centimeters. d. The mean height of male students is about 178 centimeters. e. For female students, the mean height is lower than the median height.
b. About 25% of the male students are taller than the tallest female student.
The following scatter plot presents data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed Western countries. Do these data provide strong evidence that drinking wine actually causes a reduction in heart disease deaths? a. Yes. The strong straight-line association in the plot shows that wine has a strong effect on heart disease deaths. b. No. Countries that drink lots of wine may differ in other ways from countries that drink little wine. We can't be sure the wine accounts for the difference in heart disease deaths. c. No. r does not equal -1. d. No. The plot shows that differences among countries are not large enough to be important. e. No. The plot shows that deaths go up as more alcohol from wine is consumed.
b. No. Countries that drink lots of wine may differ in other ways from countries that drink little wine. We can't be sure the wine accounts for the difference in heart disease deaths.
The risk of an investment is measured by the variability of the changes in its value over a fixed period, such as a year. More variation from year to year means more risk. The government's Securities and Exchange Commission wants to require mutual funds to tell investors how risky they are. A New York Times article says that some people think that "the proposed risk descriptions, especially one that goes by the daunting name standard deviation" are hard to understand. Explain to a friend what the standard deviation means, using the fact that the changes in a mutual fund's value over many years have a roughly Normal distribution. a. The standard deviation is the distance between the lower and upper quartiles, so it spans half the yearly changes in the fund's value. b. The standard deviation is the largest change we ever expect to see in a year. c. The yearly change in the fund's value will be greater than the standard deviation half the time and less than the standard deviation half the time. d. Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 68% of all years. e. Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 95% of all years.
d. Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 68% of all years.
The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. In this study, the response variable is a. height of researcher. b. volume of lumber. c. height of tree. d. the measuring instrument used to measure volume. e. impossible to determine.
b. volume of lumber.
