AP STATS MC
A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be -1.08. On the basis of this you would tell the college that
the college should hire a new statistician.
Event A occurs with probability 0.3, and event B occurs with probability 0.4. If A and B are independent, we may conclude that
all of the above
An assignment of probabilities must obey which of the following?
all three of the above
A consumer group surveyed the prices for a certain item in five different stores, and reported the average price as $15. We visited four of the five stores, and found the prices to be $10, $15, $15, and $25. Assuming that the consumer group is correct, what is the price of the item at the store that we did not visit?
$10
if ten executives have salaries of $80,000, six have salaries of $75,000, and three have salaries of $70,000, what is the median salary?
. $80,000
Students at University X must have one of four class ranks—freshman, sophomore, junior, or senior. At University X, 35% of the students are freshmen and 30% are sophomores. If a University X student is selected at random, the probability that he or she is either a junior or a senior is
35%
A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation. Male Female Democrat 300 600 Republican 500 300 Other 200 100 From the chart above: What is the marginal distribution for registered Democrats?
45%
A Basketball player makes 75% of his free throws. We want to estimate the probability that he makes 4 or more frees 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 throw does he hit in our first simulation of five shots? 19223 95034 58301
5
Which of the following scenarios does NOT require randomization?
All of these require randomization
A system has two components that operate in parallel, as shown in the diagram below. Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. Let F denote the event that component 1 fails during one period of operation and G denote the event that component 2 fails during one period of operation. Suppose P(F) =0.2 and P(G) = 0.03. The component failures are independent. . The event corresponding to the system failing during one period of operation is
F and G
You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked her attitude toward the product. You think there may be large differences between women who are employed outside the home and those who are not. Because of these differences, you should use
a block design
Which of the following is not a major principle of good design for all experiments?
blocking
Which statements below about least-squares regression are correct? I. Switching the explanatory and response variables will not change the least-squares regression line. II. The slope of the line is very sensitive to outliers in the x direction with large residuals. III. A value of r2 close to 1 does not guarantee that the relationship between the variables is linear.
both two and three are correct
An airline that wants to assess customer satisfaction chooses a random sample of 10 of its flights during a single month and asks all of the passengers on those flights to fill out a survey. This is an example of a
cluster sample.
When two coins are tossed, the probability of getting two heads is 0.25. This means that
in the long run two heads will occur on 25% of all tosses of two coins
Simple random sampling
none of the above
A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information you conclude
nothing, because there is no control group for comparison
A civil engineer is testing the reliability of traffic signal controllers produced by two different companies. He has 20 sets of controllers from each company, and he has been given clearance to install them at 40 different intersections in the city. He randomly assigns the controllers from company A to 20 intersections and the controllers from company B to the other intersections. The most important reason for this random assignment is that
randomization is a good way to create two groups of 20 intersections that are as similar as possible, so that comparisons can be made between the two groups.
If I toss a fair coin 5000 times
the proportion of heads will be close to 0.5
The collection of all possible outcomes of a random phenomenon is called
the sample space
Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?
. A straight line is not a good model for the data.
The interquartile range (IQR) for the number of AP courses is
2
The table below shows the results of the New Hampshire Republican Presidential Primary on January 10, 2012. Candidate Percentage of votes Mitt Romney 39 Ron Paul 23 John Huntsman 17 Rick Santorum 9 Newt Gingrich 9 Other 3 Which of the following lists of graphs are all appropriate ways of presenting these data?
Bar Graph, Pie Chart
A survey typically records many variables of interest to the researchers involved. Below are some of the variables from a survey conducted by the U.S. Postal Service. Choose the variable that is categorical.
County of residence
Consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees Centigrade) for a certain 2,000-pound car travelling 40 mph. If another data point were added with an air temperature of 0º C and a stopping distance of 80 feet, the correlation would
Decrease, since this new point is an outlier that does not follow the pattern in the data.
You open a package of plain M & M candies and count how many there are of each color. The distribution of the variable "candy color" is:
The six different colors and how many there are of each.
All but one of the following statements contains an error. Which statement could be correct?
. The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.
Other things being equal, larger automobile engines are less fuel-efficient. You are planning an experiment to study the effect of engine size (in liters) on the fuel efficiency (in miles per gallon) of sport utility vehicles. In this study,
. gas mileage is a response variable, and you expect to find a negative association.
The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.001. The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.99 for a person with the disease and 0.02 for a person without the disease. If a randomly selected person is tested and the result is positive, the probability the individual has the disease is
.047
Event A occurs with probability 0.8. The conditional probability that event B occurs, given that A occurs, is 0.5. The probability that both A and B occur
.4
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 before blue M & M's replaced tan in 1995. The probability that you draw either a brown or a green candy is
.4
One hundred high school students were asked if they had a dog, a cat, or both at home. Here are the results. If a single student is selected at random and you know she has a dog, what is the probability she also has a cat?
.75
A student is chosen at random from the River City High School student body, and the following events are recorded: M = The student is male F = The student is female B = The student ate breakfast that morning. N = The student did not eat breakfast that morning. The following tree diagram gives probabilities associated with these events.
0.30; The probability the student ate breakfast, given she is female.
The Venn diagram below describes the proportion of students who take chemistry and Spanish at Jefferson High School, Where A = Student takes chemistry and B = Students takes Spanish. Suppose one student is chosen at random. . Find the value of P(A U B)
0.6; The probability that the student takes either chemistry or Spanish, or both
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 x (bar) = 8.4, Sx= 2.1, y (bar) = 14.2, Sy = 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?
1.56
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%?
16%
For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by y(hat) = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Joseph is 22.5 months old. What is his predicted height?
79.11
A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she's been authorized to repave for this study. She decides to carry out a matched pairs experiment. Which of the following is the best way for her to carry out the randomization for this study?
Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement.
Control groups are used in experiments in order to accomplish which one of the following?
Limit the effects of variables other than the explanatory variable on the outcome.
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
Matched Pairs Experiment
Which of the following is a true statement?
Stemplots can show symmetry, gaps, clusters, and outliers.
A sample of student opinion at a Big Ten university selects an SRS of 200 of the 30,000 undergraduate students and a separate SRS of 100 of the 5,000 graduate students. What is the term for this kind of sample?
Stratified Random Sample
The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be
unchanged, equal to .52
An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that
when corn prices are above average, soybean prices also tend to be above average.
The Venn diagram below describes the proportion of students who take chemistry and Spanish at Jefferson High School, Where A = Student takes chemistry and B = Students takes Spanish. Suppose one student is chosen at random. The probability that the student takes neither Chemistry nor Spanish is
.4
A student is chosen at random from the River City High School student body, and the following events are recorded: M = The student is male F = The student is female B = The student ate breakfast that morning. N = The student did not eat breakfast that morning. The following tree diagram gives probabilities associated with these events.Given that a student who ate breakfast is selected, what is the probability that he is male?
.64
Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. The probability that at least one of the next three babies is a boy is
.875
Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. The probability that the next five babies are girls is
0.03125
For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by y(hat) = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Loretta is 20 months old and is 80 centimeters tall. What is her residual?
2.47
Mr. Williams asked the 26 seniors in his statistics class how many A.P. courses they had taken during high school. Below is a dot plot summarizing the results of his survey. Use the dotplot to determine the median number of A.P. courses taken by Mr. Williams's students is
3
Which of the following statements about influential points and outliers are true? I. An influential point always has a high residual. II. Outliers are always influential points. III. Removing an influential point always causes a marked change in either the correlation, the regression equatio n, or both.
3 only
One characteristic of roller coasters that contributes to the maximum speed of the ride is the track's maximum height. Below are computer output and a residual plot for a regression of maximum speed (in miles/hours) on maximum height (in feet) for nine roller coasters that opened recently around the world. The circled point represents a roller coaster in the Philippines whose maximum height is 70 ft. The observed speed of this roller coaster is closest to:
55
Below is computer output for calories and protein (in grams) in one cup of 11 varieties of dried beans. Predictor Coef SE Coef T P Constant 2.08 15.93 0.13 0.899 Calories 0.06297 0.02409 2.61 0.028 S = 3.37648 R-Sq = 43.2% R-Sq(adj) = 36.9% Which of the following statements is a correct interpretation of the slope of the regression line?
For each 1-unit increase in the calorie content, the predicted protein content increases by 0.063 grams.
The following numbers appear in a table of random digits: 38683 50279 38224 09844 13578 28251 12708 24684 A scientist will be measuring the total amount of leaf litter in a random sample (n = 5) of forest sites selected without replacement from a population of 45 sites. The sites are labeled 01, 02, . . . , 45 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following is correct?
Her sample is 38, 35, 02, 22, 40
A study is conducted relating AP Statistics exam scores to the total number of study hours for the AP Statistics class put in by students during the academic year, and the correlation is found to be .6. Which of the following statements is true?
Higher exam scores tend to be associated with higher numbers of study hours
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:
If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg.
A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is y(hat) = 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements must be true?
If the mean performance rating is 1.2, then the mean raise is $3800
Which of the following statements is not true?
If two events are independent, then they must be mutually exclusive
You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. "Least-squares" refers to
Minimizing the sum of the squares of the residuals.
A small company estimating its photocopying expenses finds that the mean number of copies made per day for the past 12 months is 258 copies per day with a standard deviation of 24 copies per day. Which of the following is a correct interpretation of standard deviation?
On average, the number of copies made each day was about 24 copies per day away from the mean, 258.
According to the 1990 census, those states with an above-average number of people X, who fail to complete high school tend to have an above average number of infant deaths, Y. In other words, there is a positive association between X and Y. The most plausible explanation for this is
Other variables may be confounded with variable X. For example, states with large populations may have both larger numbers of people who don't complete high school and more infant deaths.
Below is a histogram of the heights of gold-medal-winning high jumps in the Olympic Games since 1896. Which of the following is most accurate?
The median jump is between 80 and 85 inches.
The director of a fitness cneter wants to examine the effects of two exercies classes (spinning and aerobics) on body fat percentage. A six week spinning class and a six week aerobics class are offered at the same time and on the same days, so that a person can enroll in only one of them. A new class of each is about to begin and each class has 25 people in it. Ten people are randomly selected from each class. Each person's body fat percentage is measured at the beginning and again at the end of the six week class. Using the change in body fat percentage as the response variable and conducting a test, the director determines that there is a significant difference between the treatment means. Which of the following is a confounding variable in the study?
The participants' choice of which class to take
Based on the boxplot, which of the following statements is true?
The range of the middle half of the salaries is about $20,000.
A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). A least-squares line was fit to the data. Here is the residual plot from this least-squares fit. What does the residual plot tell you about the linear model?
The residual plot clearly indicates that the data isn't linear.
A Texas school district wants to compare the effectiveness of a standard AP Statistics curriculum and a new "hands-on" AP Statistics curriculum. Two experienced teachers, Mr. Pryor and Mr. Legacy, each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. Which of the following are the experimental units in this experiment?
The two students in the four classes
Economists measure the health of the real estate market is by counting "housing starts," or the number of permits issued for construction of new homes. Below is a graph displaying housing starts (in thousands) in the United States from 2006 to 2009. What is the principle weakness of this graphical presentation of data?
Using proportionally-sized pictograms exaggerates the difference between years.
Eighty volunteers who currently use a certain brand of over-the-counter allergy medication have been recruited to participate in a trial of a new allergy medication. The volunteers are randomly assigned to one of two groups. One group continues to take their current medication, the other group switches to the new experimental medication. Each is asked after two weeks if their allergy symptoms are worse, better, or about the same as they were at the start of the study. Which of the follow best describes a conclusion that can be drawn from this study?
We can determine whether the new drug reduces symptoms more than the old drug for the subjects in the study.This is the correct answer. Selected:
We say that the design of a study is biased if which of the following is true?
We say that the design of a study is biased if which of the following is true?
Suppose there are three cards in a deck, one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards at random and without replacement from the deck of three cards. The sample space S = {(1, 2), (1, 5), (2, 5)} consists of these three equally likely outcomes. Let X be the sum of the numbers on the two cards drawn. Which of the following is the correct set of probabilities for X?
X P(X) 3 1/3 6 1/3 7 1/3
