AP Stats final
A biologist is studying the effect of different nutrients and different levels of salinity (salt) in water on the growth of a certain species of fish. Ten fish are to be assigned at random to each of 12 similar tanks in a controlled environment. The biologist wants to use combinations of 2 different nutrients and 3 different salinity levels as treatments. In this experimental design, how many factors and treatments are there? A) Two factors and 6 treatments B) Two factors and 12 treatments C) Six factors and 2 treatments
A
A jar contains 10 red marbles and 15 blue marbles. If you randomly draw two marbles from the jar (without replacement), what is the probability that they are the same color? A) 0.5 B) 0.15 C) 0.52
A
A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Based on this sample, a 90% confidence interval for the mean improvement in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which of the following are the sample mean and margin of error on which this interval is based? A) Sample Mean = 13.7; Margin of Error = 1.1 B) Sample mean = 13.7; Margin of Error = 2.2 C) Sample mean is unknown; Margin of Error = 2.2
A
A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Based on this sample, a 90% confidence interval for the mean improvement μ in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which one of the following is a correct interpretation of this confidence interval? A) We are 90% confident that the true improvement in reading comprehension scores is captured by the interval 12.6 to 14.8. B) Ninety percent of the 85 sixth-graders in the sample improved their reading comprehension scores by 12.6 to 14.8 points. C) The probability is 0.90 that the true mean improvement in reading comprehension is between 12.6 and 14.8.
A
A researcher in early childhood education believes that kindergarten-age children are more receptive to help from a female teacher than from a male teacher. From a list of kindergarten teachers in the state, the researcher randomly samples four classes with male teachers and four classes with female teachers. The students in the classes are interviewed, and a measure of how receptive the students in each class are to help from the teacher is determined. This study is an example of A) an observational study. B) an experiment. C) a census.
A
A researcher is interested in the cholesterol levels of adults in the city she lives in. A cholesterol-screening program is set up in the downtown area during the lunch hour. Individuals can walk in and have their cholesterol measured for no charge. In one lunch hour, 173 people use the service, and their average cholesterol level is 217.8. The sample obtained here is an example of A) a convenience sample. B) a simple random sample, since the experimenter did not know beforehand which individuals would come to the screening. C) a stratified random sample of high- and low-cholesterol individuals.
A
A study involving women aged 50 to 75 randomly assigned equal numbers of women to an exercise program (at least 45 minutes of moderate walking or riding an exercise bike five times a week) and to a stretching program (15 to 30 minutes of stretching three times a week, under the supervision of an exercise physiologist). It was found that a higher percentage of women in the exercise group reported improved sleep than did women in the stretching group. This study is an example of A) an experiment, but not a double-blind experiment. B) a matched-pairs experiment. C) a double-blind experiment.
A
A study showed that students who spend more time studying for statistics tests tend to achieve better scores on their tests. In fact, the number of hours studied turned out to explain 81% of the observed variation in test scores among the students who participated in the study. What is the value of the correlation between the number of hours studied and test score? A) r = 0.9 B) r = 0.81 C) r = 0.656
A
An office uses two brands of fluorescent light bulbs in its overhead light fixtures. From past experience, it is known that Brand A bulbs have a mean life length of 3000 hours and a standard deviation of 200 hours, while Brand B bulbs have a mean life length of 2700 hours and a standard deviation of 250 hours. Which bulb has a longer life relative to all bulbs of its brand, a Brand A bulb that lasts 3150 hours or a Brand B bulb that lasts 2850 hours? A) The Brand A bulb has a longer life relative to its brand. B) The Brand B bulb has a longer life relative to its brand. C) The two bulbs have equally long lives.
A
Fuji apples grown at a certain orchard have a mean weight of 5.2 ounces with a standard deviation of 0.8 ounces. Suppose the scale the orchard owner uses systematically underweighs apples by 0.2 ounces and also weighs the apples in grams, rather than ounces. What would the mean and standard deviation of these apples' weights be as determined by this scale? (Note: 1 ounce ≈ 28 grams). A) Mean 140 grams, standard deviation 22.4 grams. B) Mean 140 grams, standard deviation 16.8. C) Mean 145.6 grams, standard deviation 0.8 grams.
A
In a simple random sample of 1000 Americans, it was found that 61% were satisfied with the service provided by the dealer from which they bought their car. In a simple random sample of 1000 Canadians, 58% said that they were satisfied with the service provided by their car dealer. Which of the following statements concerning the sampling variability of these statistics is true? A) The sampling variability is about the same in both cases. B) The sampling variability is much larger for the statistic based on the sample of 1000 Canadians, because Canada has a lower population density than the United States and having subjects living farther apart always increases sampling variability. C) The sampling variability is much smaller for the statistic based on the sample of 1000 Canadians because the population of Canada is smaller than that of the United States and, therefore the sample is a larger proportion of the population.
A
In a statistics class of 250 students, each student is instructed to toss a coin 20 times and record the value of , the sample proportion of heads. The instructor then makes a histogram of the 250 values of obtained. In a second statistics class of 200 students, each student is told to toss a coin 40 times and record the value of , the sample proportion of heads. The instructor then makes a histogram of the 200 values of obtained. Which of the following statements regarding the two histograms of -values is true? A) The first class's histogram has greater spread (variability) because it is derived from a smaller number of tosses per student. B) The first class's histogram has less spread (variability) because it is derived from a larger number of students. C) The first class's histogram is more biased because it is derived from a smaller number of tosses per student.
A
In the wild, 400 randomly selected blooming azalea plants are observed and classified according to flower petal color (white, pink, or orange) and whether or not they have a fragrance. The table gives the results. White Pink Orange Totals Fragrance 22 104 140 266 No Fragrance 98 16 20 134 Totals 120 120 160 400 Suppose a single azalea plant is chosen at random. Which of the following expressions establishes that the events "Fragrance" and "Pink" are not independent? A) 104/120 not equal 266/400. B) 104/400 not equal 0. C) 104/120 not equal 104/266
A
In which of the following situations would a pie chart be an appropriate graph to use to summarize your data? A) You want to display the distribution of favorite color for the students in your statistics class. B) You want to compare the percentages of students in each grade at your school who favor a certain candidate for school president. C) You want to compare the life expectancies of different professions by displaying and comparing graphs of ages at death for random samples of famous scientists, authors, actors, and politicians.
A
Suppose we classify 315 randomly selected college students according to their general major field and their self-described political viewpoint. The table presents the results. Sciences Business Humanities Social Sci Liberal 17 12 32 30 Moderate 33 40 23 20 Conservative 35 38 17 18 What percentage of all students surveyed are conservatives majoring in business? A) 12.1% B) 42.2% C) 28.6%
A
Suppose we classify 315 randomly selected college students according to their general major field and their self-described political viewpoint. The table presents the results. Sciences Business Humanities Social Sci Liberal 17 12 32 30 Moderate 33 40 23 20 Conservative 35 38 17 18 What percentage of liberals surveyed were humanities majors? A) 35.2% B) 28.9% C) 44.4%
A
Suppose we toss a fair penny and a fair nickel. Let A be the event that the penny lands heads and B be the event that the nickel lands tails. Which one of the following is true about events A and B? A) A and B are independent. B) A and B are disjoint. C) A and B are complements.
A
Suppose you take a sample of 50 students from your school and find the mean height of the students in your sample. Which one of the following does the sampling distribution of the mean describe? A) The distribution of means of all possible samples of size 50 that could be selected from the students in your school. B) The distribution of means of all samples of size 50 that have actually been selected? C) The distribution of individual heights in your sample.
A
The American Community Survey estimates that the mean household income in the United States in 2011 was $69,800, with a standard deviation of $17,000. The distribution is strongly skewed to the right. Suppose we take a simple random sample of 36 households. Which of the following is closest to the probability that the sample mean is less than $65,000? A) 0.0455 B) 0.9545 C) 0.3897
A
The daily total sales (excluding Saturday) at a small restaurant has a probability distribution that is approximately Normal with a mean of and a standard deviation of The probability the sales will exceed $700 on a given day is approximately A) 0.0778. B) 0.5778. C) 0.9222.
A
The lifetime of a 2-volt battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. The proportion of batteries with lifetimes that exceed 520 hours is approximately A) 0.4207. B) 0.5793. C) 0.2.
A
The probability of a randomly selected person being left-handed is 1/7. Which one of the following best describes what this means? A) If a very large number of people are selected, the proportion of left-handed people will be very close to 1/7. B) For every 700,000 people selected, 100,000 will be left-handed. C) If we get 4 left-handed people in 4 consecutive random selections, the probability that the next person is left-handed is substantially lower than 1/7.
A
What is the 25th percentile of the standard Normal distribution? A) -0.67 B) 0.5987 C) 1.00
A
You want to know the opinions of American high-school teachers on the issue of establishing a national proficiency test as a prerequisite for graduation from high school. You obtain a list of all high-school teachers belonging to the National Education Association (the country's largest teachers' union) and mail a survey to a random sample of 2500 teachers. In all, 1347 of the teachers return the survey. Which of the following statements about this situation is true? A) To reduce bias, you should make an effort to contact and survey the 1153 teachers who did not respond to the first mailing. B) Since you took a simple random sample, it is appropriate to draw conclusions on the basis of the teachers who responded. C) To compensate for the teachers who didn't respond to the first survey, you can take an additional random sample of 2500 different teachers and combine the results of the two surveys.
A
A blood test for a certain disease has a false positive rate of 0.01 and a false negative rate of 0.05. (Recall that "false positive" means the test returns a positive result when the subject does not have the disease). Suppose that 2% of a certain population has the disease. If a random individual from this population tests positive, what is the probability that this person actually has the disease? A) 0.019 B) 0.6597 C) 0.0288
B
A news website claims that 30% of all Major League Baseball players use performance-enhancing drugs ("PEDs") Indignant at this claim, league officials conducts a survey in which 200 randomly selected baseball players are tested. Of the tested players, 52, or 26%, test positive. Which of the following statements about this situation is true? A) The number 26% is a parameter. B) The number 26% is a statistic. C) The number 30% is a statistic.
B
A random sample of size n is collected from a Normally distributed population with standard deviation σ. Using these data, a confidence interval is computed for the mean of the population. Which of the following actions would produce a new confidence interval with a smaller width (smaller margin of error), assuming that the same data were used? A) Using a smaller sample size n B) Using a lower confidence level C) Using a higher confidence level
B
A sociologist wants to study the attitudes of American male college students toward marriage. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. All 25 men complete and return the questionnaire. Which of the following is the sample in this situation? A) All male students enrolled in Sociology 101 at this college. B) The 25 men who received and returned the questionnaire. C) American male college students.
B
At a high school with 800 students, 80% of the students ride the school bus. If 20 students are selected randomly (without replacement) and we let X = the number of students in the sample who ride the bus, then X does not exactly have a binomial distribution. Why is it nevertheless appropriate to approximate probabilities for X using the binomial distribution for n = 20 and p = 0.8? A) The binomial is always appropriate when sampling without replacement. B) Because the sample is less than 10% of the population, it is appropriate to use the binomial distribution even though the samples are not strictly independent. C) Since np > 10, we can still use the binomial distribution.
B
At a high school with 800 students, 80% of the students ride the school bus. If 20 students are selected randomly (without replacement) and we let X = the number of students in the sample who ride the bus, what is the probability that at least one of the students doesn't ride the bus? A) 0.0576 B) 0.9885 C) 0.0115
B
If X and Y are random variables, and which of the following is a condition for calculating by using ? A) X and Y are both normally distributed. B) X and Y are independent. C) X and Y are mutually exclusive.
B
In a large city, 82% of residents own a cell phone. Suppose that we randomly select three city residents. What is the probability that at least one of the three residents does not own a cell phone? [The city is large enough so that we can assume independence]. A) 0.994 B) 0.449 C) 0.006
B
In the wild, 400 randomly selected blooming azalea plants are observed and classified according to flower petal color (white, pink, or orange) and whether or not they have a fragrance. The table gives the results. White Pink Orange Totals Fragrance 22 104 140 266 No Fragrance 98 16 20 134 Totals 120 120 160 400 If a single azalea plant is selected at random and found to be orange, what is the probability that it has no fragrance? A) 0.05. B) 0.125. C) 0.149.
B
Independently selected groups of middle-school children were given a poem to memorize. After a certain period of time, they were asked to recall as much of the poem as they could. A back-to-back stemplot of the distribution of the number of words that each group of children could correctly remember is displayed below. Group 1 Group 2 1 9 2 2 8 3 1 7 3 4 31 4 02333 8 4 668 44310 5 3 755 5 0 6 Which of the following statements about these data is true? A) In general, children in Group 2 were able to recall more words than children in Group 1. B) The third quartile of the Group 1 distribution is larger than the maximum value of the Group 2 distribution (that is, 25% of the Group 1 values are larger than any Group 2 value). C) There are more students in Group 1 than in Group 2.
B
Javier's school bus is always late. Below are data on how many minutes late the bus was for 15 days in February. 1 2 2 2 3 3 4 4 4 5 6 7 8 10 12 What is the 60th percentile of this distribution? A) 3 B) 5 C) 9
B
Jerome's summer reading list has 8 books, and he is examining the number of pages in each book. After calculating the mean, median, standard deviation, and interquartile range, he realized that the longest book is actually 100 pages longer than he thought it was. Which of his measurements does he need to recalculate? A) The mean, standard deviation, and interquartile range. B) The mean and standard deviation. C) Only the mean.
B
Let X = the number of times that a randomly selected customer visits a grocery store during a one-week period. Suppose that the probability distribution of X is as follows: X 0 1 2 3 P(X) 0.1 0.4 0.4 0.1 Determine the probability that a randomly chosen customer visits the grocery store at least twice during a one-week period. A) 0.4 B) 0.5 C) 0.9
B
Ms. Kreppel is interested in the relationship between her students' final exam scores and their scores on a pre-test they took at the beginning of the year. A scatterplot of the data for the 18 students in her class shows linear relationship for these variables. The equation of the least-squares regression line is Final Exam = 34.2 + 0.60 (Pre-test) Which of the following is a correct interpretation of the slope of this regression model? A) For each one-unit increase in final exam score, the model predicts, on average, a 0.60 unit increase in pre-test score. B) For each one-unit increase in pre-test score, the model predicts, on average, a 0.60 unit increase in exam score. C) About 60% of the variation in exam score that is accounted for by the regression of exam score on pre-test score.
B
Ms. Kreppel is interested in the relationship between her students' final exam scores and their scores on a pre-test they took at the beginning of the year. A scatterplot of the data for the 18 students in her class shows linear relationship for these variables. The equation of the least-squares regression line is Final Exam = 34.2 + 0.60(Pre-test) One student scored a 76 on the pre-test and an 82 on the final exam. Which of the following is that student's residual? A) -7.4 B) 2.2 C) -2.2
B
Researchers in Britain randomly divided a large number of premature babies into three groups. One received donated breast milk, one received infant formula made for premature babies, and the third received regular infant formula. Each diet was used for one month as a sole food or as a supplement to mother's milk. Sixteen years later, the children returned and had their blood pressure measured. It was found that diastolic and systolic blood pressure both tended to be lower in the children who were fed breast milk than in the children who were fed formula. This study is an example of A) an observational study. B) an experiment. C) a census.
B
Suppose we classify 315 randomly selected college students according to their general major field and their self-described political viewpoint. The table presents the results. Sciences Business Humanities Social Sci Liberal 17 12 32 30 Moderate 33 40 23 20 Conservative 35 38 17 18 Which of the following characteristics of these data supports the conclusion that there is an association between political viewpoint and general major field? A) The marginal distributions of the two variables are not proportional. B) A higher proportion of students with a liberal political viewpoint major in the humanities, and a higher proportion of moderates and conservatives major in business. C) The sample does not contain equal number of individuals in each cell.
B
Suppose we classify 315 randomly selected college students according to their general major field and their self-described political viewpoint. The table presents the results. Sciences Business Humanities Social Sci Liberal 17 12 32 30 Moderate 33 40 23 20 Conservative 35 38 17 18 Which of the following list of numbers is a marginal distribution of the variable political viewpoint? A) 30, 20, 18 B) 91, 116, 108 C) 85, 90, 72, 68
B
The weights of cockroaches living in a university dormitory follow a Normal distribution with mean 80 grams and standard deviation 5 grams. The percentage of cockroaches having weights between 72 grams and 88 grams must be A) between 95% and 99.7%. B) between 68% and 95%. C) less than 68%.
B
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The student's expected (mean) score on this exam is A) 50. B) 25. C) 5.
B
Which of the following quantities is minimized by the least-squares regression line? A) The sum of the squares of perpendicular distances between all data points and the regression line. B) The sum of the squared differences between observed values of the response variable and values of the response variable predicted by the model. C) The sum of the squared differences between observed values of the explanatory variable and values of the explanatory variable predicted by the model.
B
Which of the following statements about the slope of the least-squares regression line is true? A) The square of the slope equals the proportion of the variation in the response variable that is explained by the explanatory variable. B) It has the same sign as the correlation coefficient r. C) It is unitless
B
Which one of the following statements is true about Student's t distribution? A) The density curve of the t distribution is symmetric and centered at the true mean of the population. B) The density curve of the t distribution has heavier "tails" than the density curve of the standard Normal distribution. C) The density curve of the t distribution more closely resembles the density curve of the standard Normal distribution when the number of degrees of freedom is small.
B
You want to perform a simulation to estimate the probability of getting at least one run of 3 heads in a row in 10 flips of a fair coin. Which of the following describes a correct simulation for estimating this probability? A) Flip a coin 10 times. Count the 10 flips as a "success" if there are at least 3 heads in that set of 10 flips. Repeat this 500 times and divide the total number of "successes" by 500. B) Assign the numbers 0 through 4 to "heads" and 5 through 9 to "tails." Read 10 one-digit numbers from a random digits table, and count this simulation as a "success" if there is at least one run of 3 or more heads. Repeat this 500 times and divide the total number of "successes" by 500. C) Assign the numbers 0 through 4 to "heads" and 5 through 9 to "tails." Read 500 1-digit numbers from a random digits table and count how many times you get runs of three or more heads in a row. Divide the count by 500.
B
A game consists of drawing three cards at random from a deck of 52 playing cards. You win 3 points for each red card that is drawn. It costs 2 points each time you play. For one play of this game, the sample space S for the net number of points you gain (after deducting the cost of play) is A) S = {0, 1, 2, 3} B) S = {0, 3, 6, 9} C) S = { -2, 1, 4, 7}
C
A high-school principal discovers a web site that invites students to "Rate Your Teacher" one a 5-point scale in several categories. He thinks this might help him decide who his best teacher are, but the school's statistics teacher tells him to ignore any information from the site. Why? A) The principle really should conduct an experiment to gather information on his teachers. B) Using a 5-point scale does not provide accurate enough information. C) Only students with particularly strong opinions—and most likely, negative opinions—are likely to take the trouble to evaluate teachers on the site.
C
A poll of American adults' opinions about efforts to reform Social Security was conducted in 2004-2005 by the AARP, the nation's largest organization for retired people. The poll results were criticized in some quarters because they included no respondents under the age of 30, even though voters aged 18 to 29 made up 17% of the 2004 electorate. By contrast, respondents aged 60 and above made up 34% of the sample but were only 24% of the electorate. This poll is most likely subject to which of the following types of bias? A) response bias B) nonresponse C) undercoverage
C
A residual plot displays a "reverse fan" arrangement, with the spread of points about the line (residual = 0) gradually decreasing from left to right (that is, as x increases). Which statement would be a correct interpretation of this plot? A) The original data display a nonlinear relationship (curved pattern of association). B) Predictions using the regression line will be more reliable for small x than for large x. C) Predictions using the regression line will be more reliable for large x than for small x.
C
A set of 10 playing cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly, and we draw 4 cards one at a time and without replacement. Let X = the number of red cards drawn. The random variable X has which of the following probability distributions? A) binomial distribution with parameters n = 4 and p = 0.5 B) binomial distribution with parameters n = 10 and p = 0.5 C) neither (A) nor (B)
C
A sociologist is studying the relationship between early childhood nutrition and academic achievement in middle school among children in a certain city. Which of the following statements about the variable "early childhood nutrition" is correct? A) Early childhood nutrition is a response variable. B) Since there is not a clear explanatory-response relationship in this scenario, we cannot classify early childhood nutrition as either explanatory or response. C) Early childhood nutrition is an explanatory variable.
C
A sociologist studying the relationship between early childhood nutrition and academic achievement in middle school among children in a certain city finds that the correlation between these two variables is 0.86. Which of the following conclusions can he draw from this study? A) Ensuring good nutrition in early childhood will increase academic achievement for middle school students. B) Since the correlation is so low, no conclusions can be drawn. C) Children in this city who have a healthy diet in early childhood tend to do better in middle school.
C
According to the 1.5 × IQR rule, how many outliers are there in the data set 72, 110, 114, 115, 118, 123, 144, 156? A) Two. B) None. C) One.
C
Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level? A) If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre. B) We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre. C) If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.
C
An agricultural scientist wants to compare the effect on yield of three different methods of growing blueberries. To control for variables such as soil condition and location, he plants 30 plots on each of six different farms. On each farm, 10 of the 30 plots are assigned to each of the three treatments (growing methods). She measures and compares the marketable yield of blueberries produced by each plot. Which of the following best describes the design of this experiment? A) a completely randomized design with three treatments B) a randomized block design with three blocks and six treatments C) a randomized block design with six blocks and three treatments
C
Consider the following five sets of outcomes from random phenomena: I. The total number of points scored in a randomly selected college football game. II. Lifespan in hours of a randomly selected halogen light bulb. III. The number of passengers in a randomly selected city bus. IV. The airline of the next plane to land at O'Hare International Airport. V. Length in inches of the next rattlesnake caught in a trap. Which of the above are continuous random variables? A) None of these are continuous random variables. B) II and III only C) II and V only
C
In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will say yes.) Which of the following is closest to the probability that you will have to ask four or more people before finding your first left-hander? A) 0.103 B) 0.147 C) 0.343
C
In a particular game, a single card is randomly chosen from a box that contains 3 red cards, 1 green card, and 6 blue card. If a red card is selected, you win $2. If a green card is selected, you win $4. If a blue card is selected, you lose $1. Let X be the amount that you win. The expected value of X is A) $1.60 B) $1.00 C) $0.40
C
In the wild, 400 randomly selected blooming azalea plants are observed and classified according to flower petal color (white, pink, or orange) and whether or not they have a fragrance. The table gives the results. White Pink Orange Totals Fragrance 22 104 140 266 No Fragrance 98 16 20 134 Totals 120 120 160 400 If a single azalea plant is selected at random, which one of the following is the probability that it has pink flower petals or no fragrance? A) 0.635. B) 0.04. C) 0.595.
C
Let X = the number of times that a randomly selected customer visits a grocery store during a one-week period. Suppose that the probability distribution of X is as follows: X 0 1 2 3 P(X) 0.1 0.4 0.4 0.1 Which of the following calculations yield the standard deviation of X, σX? A) (0.1)(0 - 1.5) + (0.4)(1 - 1.5) + (0.4)(2 - 1.5) + (0.1)(3 - 1.5) B) √(0)(0.1 - 0.25)2 + (1)(0.4 - 0.25)2 + (2)(0.4 - 0.25)2 + (3)(0.1 - 0.25)2 C) √(0.1)(0 - 1.5)2 + (0.4)(1 - 1.5)2 + (0.4)(2 - 1.5)2 + (0.1)(3 - 1.5)2
C
Let Z = the number students in Mr. Rooney's English class who arrive late on a randomly selected day. The expected value of Z is 2. Which one of the following is the best interpretation of what this means? A) We can be confident that at least 2 students will be late to Mr. Rooney's class on a randomly selected day. B) There are 2 students in Mr. Rooney's class who almost always arrive late. C) On average, the number of students who are late to Mr. Rooney's class on a randomly selected day is 2.
C
Many people believe that taking zinc lozenges reduces the severity and duration of the common cold. Sebastien decides to conduct a study at his school to explore this claim. He sends a survey to a simple random sample of 100 students, asking them to if they took zinc lozenges or not during their last cold, and how long they experienced cold symptoms. He found that students who took zinc had a mean cold duration that was 1.2 days lower than those who did not take zinc. Which of the following statements about his study is true? A) Because he only surveyed 100 students at his school, he can only draw conclusions about those 100 students. B) Because he took a random sample, Sebastien can conclude that zinc lozenges caused the reduction in cold symptoms. C) Sebastien's study is subject to confounding.
C
One of the following is a correct statement involving correlation. The other two contain blunders. Which one is correct? A) There is a correlation of r = 0.54 between the position a football player plays and his or her weight. B) The correlation between the gas mileage of a car and its weight is r = -0.71 gallon-pounds. C) The correlation between amount of fertilizer and yield of tomatoes was found to be r = 0.33.
C
Research on eating habits of families in a large city produced the following probabilities if a randomly selected household was asked "How often during the week do you have a vegetarian (meatless) main dish at dinnertime?" Outcome Probability Three + 0.06 Twice 0.10 Once 0.49 Never ? What is the probability that a randomly selected household never has a vegetarian main dish at dinnertime? A) 0 B) 0.65 C) 0.35
C
Scores on the American College Testing (ACT) college entrance exam follow a Normal distribution with mean 18 and standard deviation 6. Lisa's standardized score on the ACT was z = -0.7. What was her actual ACT score? A) 4.2. B) 22.2. C)13.8.
C
Suppose you take a sample of 50 students from your school and measure their height. Which one of the following is a random variable? A) The mean of the sampling distribution of mean heights for samples of size 50. B) The true mean height of all students from your school. C) The mean of the sample data.
C
The American Community Survey estimates that the mean household income in the United States in 2011 was $69,800, with a standard deviation of $17,000. The distribution is strongly skewed to the right. Suppose we take a simple random sample of 36 households. Which of the following accurately describes the shape of the sampling distribution of the mean household income? A) strongly skewed right—about as much as the population. B) skewed right, but not as strongly as the population. C) Approximately Normal
C
The American Community Survey estimates that the mean household income in the United States in 2011 was $69,800, with a standard deviation of $17,000. The distribution is strongly skewed to the right. Suppose we take a simple random sample of 36 households. Which of the following is closest to the 80th percentile for the sample mean? A) $72,067 B) $84,080 C) $72,180
C
The lifetime of 9-volt battery in constant use has an approximately Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Which of the following best describes the distribution of standard scores for the lifetimes of such batteries? A) Exactly Normal, with mean 0 and standard deviation 1. B) Approximately Normal, with mean 1 and standard deviation 1. C) Approximately Normal, with mean 0 and standard deviation 1.
C
The lifetime of a 9-volt battery in constant use has an approximately Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Which of the following is the approximate lifetime of a battery that lasts longer than 90% of all batteries? A) 517.28 hours B) 490.4 hours C) 541.6 hours
C
The owner of a convenience store keeps track of how many customer buy lunch food during the "noon rush" each day for four days and calculates that the mean number of customers for those four days is 52. How many customers must come in on the fifth day to make the five-day mean 54? A) 60 B) 54 C) 62
C
The stem-and-leaf diagram below gives the distribution of the ages in years of 20 participants at a family reunion. 0 7888 1 23689 2 45799 3 9 4 5 8 6 5 7 89 8 9 1 Which of the following statements about the distribution is correct? A) It makes the most sense to use the mean and standard deviation as a numerical summary of the center and spread of this distribution. B) The distribution is strongly skewed to the left. C) The mean is larger than the median.
C
The time in minutes X that you must wait before a train arrives at your local subway station is a uniformly distributed random variable that takes on values between 5 minutes and 15 minutes. That is, the density curve of the distribution of X has constant height between X = 5 and X = 15 and height 0 outside this interval. Determine P(6 < x < 8). A) 0.1 B) 0.5 C) 0.2
C
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. If the student needs at least 40 points to pass the exam, the probability that she passes is closest to A) 0.9591. B) 0.0609. C) 0.1018.
C
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation of the student's score on the exam is A) 1.94. B) 93.75. C) 9.68.
C
To examine how people respond emotionally to social media. A social scientist asks for volunteers at a local high school to fill out a survey. The survey asks how much time the subjects spent on Facebook, Twitter, and Tumblr in the last 48 hours, and then asks a series of questions that assess the subjects level of satisfaction with their lives at the present time. The scientist divides the subject up into "high social media use" and "low social media" use and then compares the satisfaction ratings of the two groups. Which of the following statements is true about this study? A) We can established whether there is a relationship between social media use and satisfaction among students at this school, but we can't establish cause and effect. B) We can determine whether social media influences satisfaction, but we can't generalize beyond the subjects of this study. C) We cannot determine whether social media influences satisfaction, nor can we generalize our findings to the entire school.
C
Which of the following best describes the purpose of replication in an experimental design? A) Repeating an experiment several times to see if results are similar. B) Reducing the impact of variables other than the treatment variable. C) Using many subjects to reduce the impact of variation arising from random assignment.
C
Which of the following is a legitimate method for taking a simple random sample of size 50 from a population of 1000 people? A) List the people alphabetically by last name. Choose a single random number between 1 and 50 using randInt(1,20) on a calculator. If, for example, that number is 16, choose the 50 people on the list in the following positions: 16, 36, 56, 76, . . .976, 996. B) List the people alphabetically by last name. Starting with the first person on the list, flip a coin. If the coin comes up "heads," that person is in the sample. Repeat this process with each person on the list until you have sample 50 people. C) Write the names of the 1000 people on slips of paper. Put the slips of paper in a (large!) hat and draw out 50 slips.
C
Which of the following probability distributions of a discrete random variable X is a legitimate probability distribution? A) x 1 2 3 p(x) 0.3 0.4 0.4 B) x -1 0 1 p(x) 0.2 0.2 0.5 C) x -1 0 1 p(x) 0.3 0.4 0.3
C
You would like to compare the level of mathematical knowledge among 15-year-olds in the United States and Japan. To do this, you plan to give a mathematics achievement test to random samples of 1000 15-year-olds in each of the two countries. To ensure that the samples will include individuals from all different socioeconomic groups and educational backgrounds, you will randomly select 200 students from low-income families, 400 students from middle-income families, and 400 students from high-income families in each country. The sampling procedure being used here is A) voluntary response sampling. B) simple random sampling. C) stratified sampling.
C
