statistics review 2
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. 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
One student from a high school will be selected at a random. Let A be the event that the selected student is a student athlete, and let B be the event that the selected student drives to school. What is the probability that the selected student will be a student athlete?
0.32
A company is considering purchasing the mineral rights to two different mountains. The probability that it will purchase the mineral rights to the first mountain is 0.55. The probability that it will purchase the mineral rights to the second mountain is 0.4. Assuming the decisions to purchase the mineral rights to each mountain are made independently, what is the probability that it will purchase the mineral rights to exactly one of the two mountains?
0.51
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
A middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two students from the club will be selected at random to participate in the county chess tournament. What is the probability that Adam and Ella will be selected?
1/10
Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. What is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy?
28/89
The Physicians' Health Study, a large medical experiment involving 22,000 male physicians, attempted to determine whether aspirin could help prevent heart attacks. Which of the following statements explains why it would not be appropriate to say that everyone should take an aspirin every other day?
I, II, and III
The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. Is Avery interpreting the probability correctly?
No, because 0.40 represents probability in the long run over many visits to the site.
According to a report for veterinarians in the United States, percent of households in the United States own dogs and percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat?
Not enough information is given to determine the probability
Researchers will use a well-designed experiment to test the effectiveness of a new drug versus a placebo in relieving symptoms of the common cold. Which of the following will provide evidence that the new drug causes relief of symptoms?
The difference between the responses to the new drug and the placebo must be shown to be statistically significant to provide evidence that the new drug causes relief
Each person in a simple random sample of 2,00 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
The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning the towels that are used daily. The manager continues this experiment for many days. Which of the following best describes the manager's study?
a completely randomized design
Which of the following can be used to show a cause-and-effect relationship between two variables?
a controlled experiment
In the design of a survey, which of the following best explains how to minimize response bias?
carefully word and field-test survey questions
An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be . A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusionot correct?
causation cannot be determined from an observational study
Mateo plays on his school basketball team. From past history, he knows that his probability of making a basket on a free throw is 0.8. Suppose he wants to create a simulation using random numbers to estimate the probability of making at least 3 baskets on his next 5 free throw attempts. Which of the following assignments of the digits 0 to 9 could be used for the simulation?
let the digits from 0 to 7 represent making a basket and the digits 8 and 9 represent not making a basket
A program exists to encourage more middle school students to major in math and science when they go to college. The organizers of the program want to estimate the proportion of students who, after completing the program, go on to major in math or science in college. The organizers will select a sample of students from a list of all students who completed the program. Which of the following sampling methods describes a stratified random sample?
randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list
A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Which of the following is NOT a legitimate concern about the procedure being used?
registered voters with unlisted telephone numbers may be underrepresented in the sample
A school nutritionist was interested in how students at a certain school would feel after taking a nutritional supplement. What possible source of bias is present in the method of data collection?
response bias where responses are self-reported
The table shows data that were collected from people who attended a certain high school basketball game and indicates the team each person rooted for and whether each of these people purchased food during the game. A person who attended the game will be selected at random. Which of the following correctly interprets mutually exclusive events represented by the table?
rooting for the home team and rooting for the away team
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
Joslyn performed an experiment using a die with its faces numbered from 1 to 6. She rolled the die and recorded whether the 5 landed face up. Suppose Joslyn could roll the die 10,000 times and keep a record of the total number of 5s landing face up in the 10,000 rolls. What would such a record illustrate?
the law of large numbers
Researchers conducted a study to investigate the effects of soft drink consumption on fat stored in muscle tissue.The people in the group who drank the soft drink had, on average, a higher percentage of fat stored in the tissue than the people who drank only water. Which of the following is the most appropriate conclusion?
there is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to adults similar to those in the study
An online customer service department estimates that about 15 percent of callers have to wait more than 8 minutes to have their calls answered by a person. Based on the simulation, what is the probability that at most 2 of the next 10 callers will have to wait more than 8 minutes to have their calls answered?
0.810
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
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
A student is applying to two different agencies for scholarships. Based on the student's academic record, the probability that the student will be awarded a scholarship from Agency A is 0.55 and the probability that the student will be awarded a scholarship from Agency B is 0.40. What is the probability that the student will be awarded at least one of the two scholarships?
0.62
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 certain monthly magazine has both print and online subscribers. Print subscribers are people who pay to have the magazine physically delivered to them each month. Which of the following is a sample of the population of interest?
50 online subscribers
For a roll of a fair die, each of the outcomes 1, 2, 3, 4, 5, or 6 is equally likely. A red die and a green die are rolled simultaneously, and the difference of the outcomes (red - green) is computed. This is repeated for a total of 500 rolls of the pair of dice. Which of the following graphs best represents the most reasonable distribution of the differences?
a graph that is unimodal and has an x-axis of -6, -4, -2, 0, 2, 4, 6
A researcher is studying the effect of genetically modified (GM) and nongenetically modified (nGM) corn on the weight gain of lambs. Which of the following designs would be best to use in the study?
a matched pairs design. For each set of twins, randomly assign one twin to the GM diet and the other to the nGM diet
The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city's effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department?
a sample survey
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 researcher selects a simple random sample of 1,200 women who are students at Midwestern colleges in the United States to use for an observational study. Which of the following describes the population to which it would be most reasonable to generalize the results?
all women who are students at Midwestern colleges in the United States
A pharmaceutical company manufactures medicine to reduce pain caused by migraine headaches. The company is investigating whether a new medicine is more effective in reducing pain than the current medicine. At the end of six months, the average pain relief for each participant was calculated. Which of the following is the best description of the study?
an experiment using a completely randomized design
Carla wants to investigate whether a person's political party affiliation causes the person to be more vocal about political issues. She plans to administer a survey to a large sample of people. Which of the following describes why the method of data collection used will prevent Carla from achieving her goal?
causation cannot be determined from a survey
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
A fair due 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
Which of the following doesnot describe a sampling method that has a potential source of voluntary response bias for the administration of a survey about college athletics at a university?
giving the survey to 30 students selected at random from each of the eight dorms on campus
A compact disc (CD) manufacturer wanted to determine which of the two different cover designs for a newly released CD will generate more sales. 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 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 B represent the event of selecting a student in the band, and let event S represent the event of selecting a student on a sports team. Are B and S mutually exclusive?
no because 5/78
To estimate the percent of red marbles in a large bag of marbles, Margo will use the following sampling method. She will randomly select a marble, record its color, put it back into the bag, shake the bag to thoroughly mix the marbles, and then repeat those steps. She will perform the procedure many times. What type of sampling method is Margo using?
random sampling with replacement
Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?
randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects
A city has designed a survey to collect information about residents' opinions about city services. Which of the following describes a scenario in which nonresponse bias is likely present?
surveys were mailed to 500 people, and 200 of the surveys were completed and returned
An experiment will be conducted in which 20 pepper plants are randomly assigned to two groups. The growth of the pepper plants will be compared for the two groups. What are the experimental units in this experiment?
the 20 plants in the two groups
Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling?
the population can be divided into strata so that the individuals in each stratum are as much alike as possible
as part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study?
the population is the 34,000 students who attend the university, and the sample is the 770 students who were selected
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 certain county school district has 15 high schools. The high school seniors' plans after graduation in each school vary greatly from one school to the next. What is one disadvantage to selecting a cluster sample to investigate the superintendent's goal?
the schools in the cluster sample might not be representative of the population of seniors
Mr. Ikeler conducted a study investigating the effectiveness of a new method for teaching a mathematics unit. He recruited 80 students at a college and randomly assigned them to two groups. What is the response variable in the study?
the score in the achievement test
As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. Let F represent the event that the selected person chose the first discount, and let S represent the event that the selected person chose the second discount. Are F and S mutually exclusive events?
yes, because the probability of F and S=0
