ap stats exam review MCQ
The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individually at retail prices. Next year's sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year's sales. What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $20 at wholesale and $30 at retail.
$220,700
Ming is learning the game of tennis and will practice serving a tennis ball within bounds. Assume that the probability of Ming serving a tennis ball within bounds is 0.40 and that her serves are independent of each other. What is the probability that the first time Ming serves a tennis ball within bounds will occur on her 4th attempt?
(0.6)^3(0.4)
In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 1/6. What is the probability that it takes three rolls until the player rolls doubles?
(1/6)(5/6)^2
A raffle for a charity fund-raiser is being planned. Each of 2000 raffle tickets will be sold for $1.00. The holders of 32 winning tickets will each win a prize. The table shows the prize values and the number of prizes for each value. The random variable � represents the value of the prize won for a single ticket minus the cost of the ticket. What is the expected value of �?
-$.20
Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?
0
A fair coin is flipped 10 times and the number of heads is counted. This procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?
0,0,6,9,22,24,18,12,7,2,0
A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?
0.0195
A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?
0.023
Joe and Matthew plan to visit a bookstore. Based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below. Assuming that Joe and Matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?
0.1250
In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course?
0.13
The following question(s) refer to the following information.Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?
0.14
The following question(s) refer to the following information.Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00? Responses
0.14
At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds? Responses
0.17
The distribution of colors of candies in a bag is as follows. If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?
0.22
One student from a high school will be selected at random. Let � be the event that the selected student is a student athlete, and let � be the event that the selected student drives to school. If �(�∩�)=0.08 and �(�|�)=0.25, what is the probability that the selected student will be a student athlete?
0.32
For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?
0.335
The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times?
0.37
Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt 5 shots of the arrow and that each shot is independent from the others. Let the random variable X represent the number of times he hits the inner ring of the target in 5 attempts. The probability distribution of X is given in the table. What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X ?
0.40951
A distribution of scores is approximately normal with a mean of 78 and a standard deviation of 8.6. Which of the following equations can be used to find the score x above which 33 percent of the scores fall?
0.44=r-78/8.6
A die used in a certain board game has eight faces, of which 3 are red, 3 are yellow, and 2 are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. For example, a player who tosses the sequence shown in the following table has tossed the die 3 times before blue lands faceup. What is the probability that a player will toss the die at least 2 times before blue lands faceup? Responses
0.5625
In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. One car will be selected at random from the parking lot. If each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green?
0.6
At a sporting event, cheerleaders will throw 50 bundled T-shirts into the crowd. The T-shirt sizes consist of 10 small, 15 medium, and the remainder either large or extra large. Suppose Ana catches a T-shirt. What is the probability that she will catch a T-shirt that is not a size small?
0.80
A police officer is using a radar device to check motorists' speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer's estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?
0.8704
Luisa is a manager at a pet insurance company with many customers. Sixty percent of the company's customers filed claims in the past year. Luisa will randomly select 12 customers from all the company's customers. Assuming the customers selected are independent of each other, which of the following is closest to the probability that more than 2 of the 12 customers sampled did not file claims in the past year? Responses
0.917
A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?
0.922
An exponential relationship exists between the explanatory variable and the response variable in a set of data. The common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of log(�^)=7.3−1.5�. Which of the following is closest to the predicted value of the response variable for �=4.8 ?
1.26
Which of the following is the best estimate of the standard deviation of the distribution shown in the figure above?
10
The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg?
12%
Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange. Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?
13.75 and 2.905
Ninety percent of the people who have a particular disease will have a positive result on a given diagnostic test. Ninety percent of the people who do not have the disease will have a negative result on this test. If 5 percent of a certain population has the disease, what percent of that population would test positive for the disease? Responses
14%
There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model ŷ = 25.2 + 3.3x 9 < x < 25, where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?
16.5 ° F
Each accountant at a large accounting firm was classified according to accountant level (junior or senior) and method of transportation to work (walk, bus, drive alone, or carpool). The responses of the 320 accountants at the firm are summarized in the table. What proportion of the accountants at the firm are at the senior level and carpool to work?
20/320
The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades by the National Hurricane Center. Summary measures are shown below. Min = 12 Max = 24 Lower quartile = 15 Upper quartile = 18 Median = 16 n = 10 Which of the following statements is true?
24 is an outlier and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.
The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution?
26 inches
Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?
3/15
The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3-year-old boys.Duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. Shane is 34.0 inches tall and is at the 62nd percentile of the distribution. Which of the following is closest to the mean of the height distribution?
33.21 inches
The seniors at three high schools were surveyed about their plans after graduation. The following table shows the responses, classified by high school. One senior from the high schools will be selected at random. What is the probability that the senior selected will not be from High School B given that the senior responded with a choice other than college?
396/538
A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent of the women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements?
42
The relationship between carbon dioxide emissions and fuel efficiency of a certain car can be modeled by the least-squares regression equation ln(�^)=7−0.045�, where � represents the fuel efficiency, in miles per gallon, and �^ represents the predicted carbon dioxide emissions, in grams per mile. Which of the following is closest to the predicted carbon dioxide emissions, in grams per mile, for a car of this type with a fuel efficiency of 20 miles per gallon?
446
The probability that a particular electrical component operates successfully is 3/4. An electrical system consists of three such components that operate independently. The system will function successfully if at least one of the three components operates successfully. What is the probability that the system will function successfully?
63/64
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to
70
A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg).If the manager's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?
700 mg to 740 mg
Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z = -1.2. What score did this student receive on the test? Responses
779.42
The following question(s) refer to the following information.Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If the customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?
9.40
On-base percentage plus slugging (OPS) is a statistic used in baseball to measure a team's batting success. The number of runs scored and OPS for 30 baseball teams was used to conduct a linear regression analysis. The scatterplot and computer output for the regression analysis is shown. Which of the following is the most appropriate interpretation of the statistic 93.47% in the regression output?
93.47% of the variation in number of runs scored can be explained by the linear regression with OPS.
A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company's claim is correct, what is the expected number of nondefective lightbulbs in a random sample of 1,000 bulbs? Responses
980
A paint manufacturer conducted an experiment to investigate whether a new formula produces paint that lasts longer on the exterior of a building than paint produced using an older formula. A grid of 20 squares was drawn on one side of an exterior wall of a building. The new formula was randomly assigned to 10 squares, and the older formula was assigned to the remaining 10 squares. Each square was painted with the assigned formula. One year later, each square was rated on how well the paint had lasted, using a numerical scale for which larger values indicated longer-lasting paint.
A completely randomized design, because each formula was randomly assigned to 10 squares.
Which of the following can be used to show a cause-and-effect relationship between two variables?
A controlled experiment
For which of the following distributions is the proportion of values between 900 and 1,000 the greatest?
A normal distribution with mean 950 and standard deviation
At a certain clothing store, the clothes are displayed on racks. The clothes on each rack have similar prices, but the prices among the racks are very different. To estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. What type of sample is the consumer selecting?
A stratified random sample
A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed in water with the new powder; otherwise, the rose was placed in water alone. Which of the following is the best description of the method used by the florist? Responses
An experiment with a completely randomized design
A company determines the mean and standard deviation of the number of sick days taken by its employees in one year. Which of the following is the best description of the standard deviation?
Approximately the mean distance between the number of sick days taken by individual employees and the mean number of sick days taken by all employees
A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this?
Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.
In the design of a survey, which of the following best explains how to minimize response bias?
Carefully word and field-test survey questions.
A certain county has 1,000 farms. Corn is grown on 100 of these farms but on none of the others. In order to estimate the total farm acreage of corn for the country, two plans are proposed. Plan I: Sample 20 farms at random. Estimate the mean acreage of corn per farm in a confidence interval. Multiply both ends of the interval by 1,000 to get an interval estimate of the total. Plan II: Identify the 100 corn-growing farms. Sample 20 corn-growing farms at random. Estimate the mean acreage of corn for corn-growing farms in a confidence interval. Multiply both ends of the interval by 100 to get an interval estimate of the total. On the basis of the information given, which of the following is the better method for estimating the total farm acreage of corn for the county?
Choose plan II over plan I.
The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store's primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then opens the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and determines the proportion of the 150 controllers that are defective. What type of sample is this?
Cluster random sample
A company that sells baby food is interested in the baby food preferences of all families with toddlers from a certain city. A representative from the company sets up a booth at one grocery store in the city that will be used to investigate baby food preference. The representative will ask people with toddlers who walk past the booth to complete the survey. Which of the following best describes the sampling method the company will use?
Convenience sampling
The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that the probability of being awarded the first job (event A) is 0.75; the probability of being awarded the second job (event B) is 0.5; and the probability of being awarded both jobs (event (A and B)) is 0.375. If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B ?
Event A and event B are not mutually exclusive and are independent.
A store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68. Which of the following is the best interpretation of the probability 0.68 ?
For all customers who purchase a lawn mower, 68% will also purchase an extended warranty.
Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males. Based on the computer output above, which of the following is the best interpretation of the value of the slope of the regression line?
For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 22.563 calories per day
A field researcher who studies lions conjectured that the more time a cub spends playing, the sooner the cub will begin to hunt. Observational data were collected from 20 lion cubs. The researcher recorded how long they spent playing and the age when they began hunting. Because male and female lions have different hunting behaviors, the researcher recorded the data for males and females separately. The two scatterplots show the data for the 10 female lions and the 10 male lions. Based on the scatterplots, for which gender does there appear to be evidence that the more time a lion cub spends playing, the sooner the cub is likely to begin hunting?
For female cubs only
A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ?
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3.
Gina's doctor told her that the standardized score (z- score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.50. Which of the following is the best interpretation of this standardized score?
Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
Consider a data set of positive values, at least two of which are not equal. Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1? The mean The median The standard deviation
I, II and III
The Physicians' Health Study, a large medical experiment involving 22,000 male physicians, attempted to determine whether aspirin could help prevent heart attacks. In this study, one group of about 11,000 physicians took an aspirin every other day, while a control group took a placebo. After several years, it was determined that the physicians in the group that took aspirin had significantly fewer heart attacks than the physicians in the control group. Which of the following statements explains why it would not be appropriate to say that everyone should take an aspirin every other day? The study included only physicians, and different results may occur in individuals in other occupations. The study included only males and there may be different results for females. Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health.
I, II, and III
An experiment was conducted to investigate whether submersion in cold water causes a lower heart rate. The experiment used 50 volunteers. The 25 youngest volunteers had their heart rate measured while holding their breath for 30 seconds with their face submerged in cold water. The 25 oldest volunteers had their heart rate measured while holding their breath for 30 seconds with their face not submerged in cold water. The mean heart rate for volunteers who had their face submerged in cold water was lower than the mean heart rate for volunteers who did not have their face submerged in cold water. Which of the following elements of a well-designed experiment is missing? Comparison of at least two treatment groups Random assignment of treatments to experimental units Replication
II only
The boxplots above summarize two data sets, A and B. Which of the following must be true? Set A contains more data than Set B. The box of Set A contains more data than the box of Set B. The data in Set A have a larger range than the data in Set B.
III only
Data on homes recently sold in a certain town included the area of the home, reported in square feet. The table below shows summary statistics of the reported areas, in square feet. An auditor determined that an error was made in the reported areas and that all of the areas should have been 100 square feet greater than what was reported. The areas were corrected and new summary statistics were reported. What are the interquartile range (IQR) and the standard deviation of the corrected areas?
IQR 102, standard deviation 61.0723
A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table below.
If the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.
A local employer asked for help selecting a new type of desk chair. Thirty employees volunteered, and each employee used the new desk chair for two weeks and the current desk chair for two weeks. To determine which chair was used first, a coin was flipped for each employee. Heads represented using the new chair first, and tails represented using the current chair first. At the end of each two-week period, the employees were asked to rate their satisfaction with the new chair. Which of the following best describes this study?
It is a well-designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.
Heights, in inches, for the 200 graduating seniors from Washington High School are summarized in the frequency table below. Which of the following statements about the median height is true?
It is greater than or equal to 60 inches but less than 66 inches.
A compact disc (CD) manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion?
It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.
A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days. Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?
Machine A usually, but not always, produced fewer defective parts than machine B.
The distribution of random variable � has mean 10 and standard deviation 4. The distribution of random variable � has mean 7 and standard deviation 3. If � and � are independent, what are the mean and standard deviation of the distribution of �−� ?
Mean 3 and standard deviation 5
A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made?
Median
The boxplot summarizes the reading rates, in words per minute (wpm), for 160 elementary school students. Based on the boxplot, which of the following statements is not true for the data set?
More students had reading rates between 30 wpm and 52 wpm than between 52 wpm and 70 wpm.
For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long?
No, because 3 inches falls above the maximum value of lengths in the sample.
To check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design?
No, because temperature is confounded with brand.
A researcher collected data on the age, in years, and the growth of sea turtles. The following graph is a residual plot of the regression of growth versus age. Does the residual plot support the appropriateness of a linear model?
No, because the graph displays a U-shaped pattern.
A high school science teacher has 78 students. Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let event � represent the event of selecting a student in the band, and let event � represent the event of selecting a student on a sports team. Are � and � mutually exclusive events?
No, because �(�∩�)=578.
The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 60 students. Which of the following survey methods will produce a simple random sample?
Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.
Let random variable � represent the the number of visitors to a certain museum during a given day. The following table shows the probability distribution of the random variable. Which of the following claims about the distribution of random variable � is best supported by the histogram?
On a given day, it is equally likely for the museum to have less than 300 visitors as it is to have more than 300 visitors.
Let the random variable � represent the number of students who go to a certain teacher's office hour each day. The standard deviation of � is 2.2. Which of the following is the best interpretation of the standard deviation?
On average, the number of students going to an office hour varies from the mean by about 2.2 students.
A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized?
Only people aged nineteen to thirty living in the state of Colorado
A randomized block design will be used in an experiment to compare two lotions that protect people from getting sunburned. Which of the following should guide the formation of the blocks?
Participants within each block should be as similar as possible with respect to how easily they get sunburned.
The owner of a food store conducted a study to investigate whether displaying organic fruit at the front of the store rather than at the back of the store will increase sales of the fruit. At the beginning of each week, the organic fruit display was randomly assigned to either the front or the back of the store, and sales for the week were recorded. At the end of 12 months, the owner determined that the average weekly sales of organic fruit displayed at the front of the store were greater than the average weekly sales of organic fruit displayed at the back of the store. The difference was statistically significant. What can be concluded from the study?
Placing the display at the front instead of the back of the store causes an increase, on average, of weekly sales of the organic fruit.
A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows: Generate a random integer from 1 to 20. Use that integer to select an initial box from the first 20 boxes in line on the conveyor belt. Select every 25th box that follows the initial box on the conveyor belt for the rest of the day. Which of the following best describes the proposed sampling method?
Systematic random sample
Data were collected on two variables, � and �, to create a model to predict � from �. A scatterplot of the collected data revealed a curved pattern with a possible cubic relationship (�=��3, where � is a constant) between the variables. Which of the following transformations would be most appropriate for creating linearity between the variables?
Taking the log of both x and y
An experiment will be conducted to determine whether children learn their multiplication facts better by practicing with flash cards or by practicing on a computer. Children who volunteer for the experiment will be randomly assigned to one of the two treatments. Because the children's gender may affect the outcome, there will be blocking by gender. After practice, the children will be given a test on their multiplication facts. Why will it be impossible to conduct a double-blind experiment?
The child will know whether he or she used flash cards or the computer.
A common measure of flexibility is the sit-and-reach test, where a person sits on the floor with legs straight in front. The person then reaches as far forward as possible, and the distance reached past the feet is recorded. The histograms summarize the results of the sit-and-reach test for two groups, young adult men and middle-aged men. Negative distances represent a reach that is not as far as the feet. Which of the following statements is the best description of the distributions of distances?
The distribution for young adult men is skewed to the left, and the distribution for middle-aged men is approximately symmetric.
The histogram above shows the number of minutes needed by 45 students to finish playing a computer game. Which of the following statements is correct?
The distribution is skewed to the left.
The back-to-back stem-and-leaf plot below gives the percentage of students who dropped out of school at each of the 49 high schools in a large metropolitan school district. Which of the following statements is NOT justified by these data?
The drop-out rate decreased in each of the 49 schools between the 1989-90 and 1992-1993 school years.
As part of a community service program, students in three middle school grades (grade 6, grade 7, grade 8) each chose to participate in one of three school-sponsored volunteer activities. The graph below shows the distribution for each class for the three activities. Based on the graph, which statement must be true?
The grade with the greatest percentage of students who chose activity C was grade 8.
An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree. predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases, on average, by 0.48 meter each year.
One statistic calculated for pitchers in baseball is called the earned run average, or ERA. The following boxplots summarize the ERA for pitchers in two leagues, A and B. Based on the boxplots, which of the following statistics is the same for both leagues?
The interquartile range
Each person in a random sample of adults was asked how many DVDs he or she owned. Summary statistics are given below. Which of the following statements is true?
The interquartile range of the number of DVDs owned is 65.
A city planner is investigating traffic congestion at a certain intersection. To collect data, a camera will record the number of cars that pass through the intersection at different hours of the day and on different days of the week. Which of the following best describes the type of investigation being conducted by the city planner?
The investigation is an observational study because treatments are not imposed.
In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014, let the random variable � represent the number of households in the sample that had a computer. What are the mean and standard deviation of � ?
The mean is 170 households, and the standard deviation is 5.05 households.
The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ?
The mean is 22 and the standard deviation is 100.
For a random sample of 50 newborn Holstein calves from the United States, the mean weight was 80 pounds and the standard deviation was 6 pounds. In order to compare these findings with those of other countries, an agricultural engineer converted the measured calf weights from pounds to kilograms by multiplying each weight by 0.454. What are the mean and standard deviation of the converted weights of the 50 newborn Holstein calves?
The mean weight is 36.32 kilograms and the standard deviation is 2.724 kilograms.
In northwest Pennsylvania, a zoologist recorded the ages, in months, of 55 bears and whether each bear was male or female. The data are shown in the back-to-back stem plot below.
The median age and the range of ages are both greater for female bears than for male bears.
The distribution of housing prices in a city includes several outliers at the upper end of the distribution and no outliers at the lower end of the distribution. Which of the following is the most resistant, or robust, measure of center of the distribution of housing prices?
The median, because it is not greatly affected by the outliers.
A veterinarian interested in pet nutrition surveyed owners of a single pet (either a dog, a cat, or a ferret) to ask whether they feed their pet primarily dry pet food, canned pet food, or home-cooked food. The following segmented bar graph shows the distribution of the three types of food for each type of pet. Which of the following statements about pet owners in the survey is supported by the segmented bar graph?
The number of ferret owners who fed their pets primarily dry pet food was equal to the number of ferret owners who fed their pets primarily home-cooked food.
The director of a fitness center wants to examine the effects of two exercise 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 at the a = 0.01 level, 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.
A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant?
The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant.
The following table shows the classification of all 51 dogs from an animal shelter by whether the dogs lived mostly outdoors or mostly indoors before coming to the shelter and whether they tested positive or negative for a certain skin condition. One dog from the animal shelter will be selected at random. Based on the table, which of the following statements is correct?
The probability of selecting a dog that tested positive given that the dog lived mostly outdoors is less than the probability of selecting a dog that tested positive given that the dog lived mostly indoors.
The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
The proportion of the variation in height that is explained by a regression on age is 0.64.
A data set of test scores is being transformed by applying the following rule to each of the raw scores. Transformed score = 3.5(raw score) + 6.2 Which of the following is NOT true?
The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2.
Caleb designed an experiment to investigate whether listening to music or chewing gum affects the time to complete a level of a certain video game. Before the game started, each person in a sample was randomly assigned to either listen to music or not listen to music. Each person was also randomly assigned to either chew gum or not chew gum. At the end of the game, the time to complete the level for each person in the sample was recorded. Which of the following correctly identifies the response variable of the experiment and whether the variable is categorical or quantitative?
The response variable is the time to complete the level and the variable is quantitative.
A researcher conducted an experiment to study the effects of an herbal supplement on the duration of the common cold. From a sample of 50 people who had a cold, the researcher assigned 25 people to take the supplement each day. The other 25 people were asked to drink water each day and were not given the supplement. The researcher recorded the number of days the cold lasted for each person. What are the experimental units of the study?
The sample of 50 people who had a cold
A scatterplot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true?
The slope of the least squares regression line increases and the correlation coefficient increases.
Which of the following statements must be true about the data sets A and B displayed in the histograms above?
The standard deviation of data set A is greater than the standard deviation of data set B.
At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?
The student did equally well in each course.
The tail length of Siberian tigers is approximately normally distributed with a mean of 0.85 meter and a standard deviation of 0.13 meter. Which of the following is the best interpretation of the �-score for a particular Siberian tiger with a tail length of 0.8 meter?
The tiger's tail length is approximately 0.38 standard deviation below the mean.
A sample of 15 golfers who played a golf course on a certain day was selected. For each golfer, the average driving distance (�), in yards, and the percent of fairways hit on the drive (�) were recorded. The scatterplot displays the percent of fairways hit versus the average driving distance. Also shown is the least-squares regression line, �^=66.228+0.0002�. The point circled on the scatterplot is considered an influential point. A new least-squares regression line will be calculated with the influential point removed. How will the removal of the influential point affect the new least-squares regression line for the remaining 14 points?
The �-intercept will increase, and the slope will be negative.
A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the number of students by employment status (job, no job), and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?
There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.
For a middle school science project, Jalen measured the pH of 25 vinegar products. The summary statistics for the values of the pH are shown in the following computer output. Based on the 1.5×IQR rule for outliers, which of the following statements is true?
There are no pH values that could be identified as outliers.
A recent study examined 699 car accidents in Toronto over a fourteen-month period. Records of phone-service providers were used to determine whether the driver was using a cell phone during or immediately before the accident. Overall, the researchers found that drivers using cell phones were 4.3 times as likely to have an accident as drivers who were not using cell phones. The result was statistically significant. Which of the following can be concluded from this study?
There is an association between cell phone use and accidents, but not necessarily a causal relationship.
A tennis ball was thrown in the air. The height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. The correlation between the time and height was computed to be 0. What does this correlation suggest about the relationship between the time and height?
There is no linear relationship between time and height.
At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution? Responses.
There were 770 entries with a score less than or equal to 68.
Each person in a simple random sample of 2,000 received a survey, and 317 people returned their survey. How could nonresponse cause the results of the survey to be biased?
Those who did respond may differ in some important way from those who did not respond.
A regional transportation authority is interested in estimating the mean number of minutes working adults in the region spend commuting to work on a typical day. A random sample of working adults will be selected from each of three strata: urban, suburban, and rural. Selected individuals will be asked the number of minutes they spend commuting to work on a typical day. Why is stratification used in this situation?
To decrease the variability in estimates of the mean commuting time
The following table shows data for the 8 longest roller coasters in the world as of 2015. Which of the following variables is categorical? Responses
Type
Administrators at a state university computed the mean GPA (grade point average) for juniors and seniors majoring in either physics or chemistry. The results are displayed in the table below. When juniors and seniors are grouped together, could physics majors have a higher mean GPA than chemistry majors?
Yes. It could happen. Whether it does happen depends on the variability of the GPAs within each of the four groups of students.
For which of the following distributions is the mean greater than the median?
a
The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?
n=10 only
In a large set of data that are approximately normally distributed, r is the value in the data set that has a z-score of -1.00 s is the value of the first quartile, and t is the value of the 20th percentile. Which of the following is the correct order from least to greatest for the values of r, s, and t ?
r, t, s
The distribution of weight of a small watermelon is known to have a mean of 5 pounds and a standard deviation of 1.2 pounds. Six small watermelons fit in a crate, and the crate weighs exactly 1 pound. Assuming the weights of small watermelons are independent, what is the standard deviation of the total weight of a random sample of 6 small watermelons and the crate?
sq 6(1.2)^2
Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student had a standardized score of z = 1.72 before the conversion, what is the standardized score for the student after the conversion? Responses
z = 1.72
The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread?
µ = 15.93, σ = 0.46
Consider n pairs of numbers (x1,y1), (x2,y2), ..., and (xn, yn). The mean and standard deviation of the x-values are x̄ =5 and sx = 4, respectively. The mean and standard deviation of the y-values are ȳ = 10 and sy = 10 respectively. Of the following, which could be the least squares regression line?
ŷ = 8.5 + 0.3x
