AP STATS UNIT 3 TERMS AND MCQ
simple random sample
each set of n elements in the population has an equal chance of selection
Population
intended group, all residents of ____
Voluntary response bias
introduced when individuals can chose on their own to participate in the sample, not recoverable
a stratified random sample
is a more complex type of probability sampling where we first divide the population into groups of similiar individuals called strata then we choose a separate SRS and each Stratham and combine these SRSS to form the full
response variable (in regards to simulation)
values of this record the results of each trial with respect to what we were interested in
Sample
those who actually respond
In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was ŷ = 10 + 0.9x where ŷ is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?
(d) 95.5
When working on a table of random digits and you need 50 labels, use ___-___
01-50
Matched pairs method of sampling is used to compare _____ treatments
2
Random number generator
A device that is used to generate random numbers
Kristen is investigating the opinions of students at her high school on the new school hours proposed by the school board. Which of the following is her population of interest?
All students at her high school
Blinding
Any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups -1. People who can influence the results -2. People who evaluate the results
Statistic
Any information drawn from a sample
Parameter
Any information drawn from an entire population
Double-blind
Both classes are blinded during he experiment
A sample of students will be selected from all the students at a high school. Which of the following sampling methods is least likely to produce a representative sample of the students?
From a randomly chosen home basketball game, choose every tenth student who enters the gymnasium.
Participants
Humans who are being experimented on
The manager of a shopping mall distributed a customer-satisfaction survey by handing it to people as they came through one of the doors to the mall one day. Of those handed out, 215 were completed and returned. Should the results of the survey be generalized to the population of all customers of the shopping mall?
No, because a random sample from all customers of the shopping mall was not selected.
Simple Random Sample
Not only does in the population have an equal chance of being selected but every combination of people has an equal chance of being selected
Random numbers
Numbers selected at random without bias
Single-blind
One of the two classes are blinded during the experiment
Placebo effect
Subjects unknowingly given a placebo and report their treatment had an effect
Treatment
The combination of specific levels from all the factors that an experimental unit receives
Which of the following is a benefit to using a random sample for an observational study?
The results of the observational study can be generalized to the population.
random
an event is this if we know what outcomes could happen, but not which particular values will happen
outcome
an individual result of a component of a simulation
matching
any attempt to force a sample to resemble specified attributes of the population
blinding
any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups
nonresponse bias
bias created when people who are randomly selected refuse to particiapte in the sample
Name the sampling strategy: Randomly select 10 stores around the country and survey all the employees that work at those stores.
cluster sample
voluntary response sample
consist of individuals who decide themselves whether or not they want to be part of the sample
convenience sampling
consists of choosing individuals that are easiest to reach
convenience sample
consists of the individuals who are conveniently available
Undercoverage
design flaw that leaves a part of the population out or gives a part of the population less representation, can recover if you can identify and go after them
experimental units
individuals on whom an experiment is performed
Probability sample
is a sample chosen by chance we must know what samples are possible and what chance or probability each possible sample has
simulation
models random events by using random numbers to specify event outcomes with relative frequencies that correspond to the true real-world relative frequencies we are trying to model
An advantage to a stratified sample
more demographics/regions can be represented
observational study
observes individuals and measures variables of interest but only as an observer
Example of matched pairs
one new shoe and one old shoe to test the efficiency of the new shoes
stratified random sample
population is divided into homogenous groups and then a random sample is drawn from each group
Generating random digits on your calculator
rand Int(starting, ending, how many at a time)
multistage sampling
sampling schemes that combine several different sampling methods at different stages
Name the sampling strategy: Each employee has a 3-digit identification number. Randomly chose 40 numbers.
simple random sample
undercoverage
some portion of the intended population is either unrepresented or under-represented
blocking
subjects or experimental units are grouped together homogeneously because of some charcteristic they have in common that is believed might effect the experiment
randomization
the best defense against bias, in which each individual is given a fair, random chance of selection
sampling variability
the natural tendency of randomly drawn samples to differ
Lurking variable
variable associated with both y and x that makes it appear that x may be causing y
Confounding variable
variable whose effects on y can't be distinguished from the effect of x
statistically significant
when an observed difference is too large for us to believe that is is likely to have occurred naturally
double-blind
when both those who could influence and evaluate the results are blinded
A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μ and variance σ2 of a single roll are 3.5 and 2.92, respectively. What is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2?
√2.92/5+2.92/10
placebo
a fake treatment often given to the control group to help prevent the placebo effect (subjects improving by the power of suggestion)
census
a sample that consists of the entire population
census
attempting to survey the entire population
3 principles of experimental design
control, randomization, replication
principles of experimental design
control, randomize, replicate, block
randomized block design
randomization occurring within blocks
treatment
the process, intervention, etc that is applied to each subject in an experiment
response variable
the variable that will be measured in an experiment
block
when groups of experimental units are similar, it is a good idea to gather them together into these
confounded
when the levels of one factor are associated with the levels of another factor so their effects cannot be separated
confounding
when the results of an experiment can be determined because a variable has not be accounted for and has interferred with your results
double blind
when the subjects as well as those evaluating the result of an experiment do not know which subjects are in the treatment or control groups
Convenience
A sample that consists of individuals who are conveniently available
Which of the following is not a major principle of good design for all experiments? A. comparison to a control B. replication C. blocking D. randomization E. all of these are significant for every experiment
C. blocking
Recipes for the same type of cookies can vary in terms of ingredients and baking times. From a collection of chocolate chip cookie recipes, a baker randomly selected 5 recipes. From a collection of oatmeal raisin cookie recipes, the baker randomly selected 4 recipes. The mean baking times, in minutes, for each sample were recorded as x¯C and x¯O, respectively. What is the correct unit of measure for the standard deviation of the sampling distribution of x¯C−x¯O?
Minutes
A certain company has five departments, A, B, C, D, and E. The number of employees in each department is 10, 10, 20, 30, and 30, respectively. A sample of 10 employees from all employees will be selected. Of the following descriptions of sampling procedures, which is most likely to introduce a potential source of bias?
Randomly select 10 employees from department C
Confounding
The levels of one factor are associated with levels of another factor
A stratified random sample addresses the same issues as which of the following experimental designs? A. a block design B. a double-blind experiment C. an experiment with a placebo D. a matched pairs design E. a confounded, nonrandomized study
A. a block design
In an experiment, the primary purpose of blinding is to reduce A. bias B. confounding C. randomness D. under-coverage E. variation
A. bias
Random Sample
Everyone in the population has an equal chance of of being selected
Multistage
Sampling methods that involve more than one sampling method
3 requirements of an SRS
label, randomize, select
cluster sample
population is split into parts or clusters usually based on geography and then entire clusters are selected randomly and sampled
response variable
values of this variable record the results of each trial with respect to what we were interested in
single-blind
when either those who could influence or evaluate the results is blinded
Which of the following are true statements? 1. voluntary response samples often underrepresent people with strong opinions 2. convenience samples with non-neutral wording often lead to under coverage bias 3. questionnaires with non-neutral wording are likely to have response bias A. 1 and 2 B. 1 and 3 C. 2 and 3 D. 1, 2, and 3 E. none of the above give the correct set of responses
C. 2 and 3
In an experiment, an observed effect so large that it would rarely occur by chance is called A. an outlier B. influential C. statistically significant D. bias E. replication
C. statistically significant
Sampling surveys
Designed to ask questions to a small group of people in the hope of learning something about he entire population
Can watching a movie temporarily raise your pulse rate? Researchers have 50 volunteers check their pulse rates. Then they watch an action film, after which they take their pulse rates once more. Which aspect of experimentation is present in this research? A. a placebo B. blinding C. randomization D. a control group E. none of these
E. none of these
Sample Size
The number of trials earned out in a sample
trial
the sequence of several components representing events that we are pretending will take place
A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number of service calls in a month at y x each location. Summary calculations give x=8.4, œ sx=2.1, y=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?
(b) 1.56 (based on equation for b)
A local tax reform group polls the residents of the school district and asks the question, "Do you think the school board should stop spending taxpayers' money on non-essential arts programs in elementary schools?" The results of this poll are likely to A. underestimate support for arts programs because of undercoverage B. underestimate support for arts programs because of non-sampling error C. overestimate support for arts programs because of undercoverage D. overestimate support for arts programs because of non-sampling error E. accurately estimate support for arts programs
B. underestimate support for arts programs because of non-sampling error
Consider two populations of coins, one of pennies and one of quarters. A random sample of 25 pennies was selected, and the mean age of the sample was 32 years. A random sample of 35 quarters was taken, and the mean age of the sample was 19 years. For the sampling distribution of the difference in sample means, have the conditions for normality been met?
No, the conditions for normality have not been met because the sample size for the pennies is not large enough and no information is given about the distributions of the populations.
prospective study
a study where we collect data as it happens
voluntary response
bias where we allow members of our population to respond at will
population
the entire group of individuals or instances about whom we hope to learn
level
the experimental values that are chosen for each factor
Which of the following statements are true? I. Correlation requires one variable to be identified as the explanatory variable and other as the response variable. II. A two-variable scatterplot requires that both variables be quantitative. III. Every least-square regression line passes through (x , y). (a) I and II only (b) I and III only (c) II and III only (d) I, II, and III (e) None of the above
(c) II and III only
The following are resistant: (a) Least squares regression line (b) Correlation coefficient (c) Both the least square line and the correlation coefficient (d) Neither the least square line nor the correlation coefficient (e) It depends
(d) Neither the least square line nor the correlation coefficient
An experiment compared the adhesion of 2 types of paint, A and B, to 3 types of metal, 1, 2, and 3, used in automobiles. Thirty sheets of metal were used in the experiment: 10 of Metal 1, 10 of Metal 2, and 10 of Metal 3. Half of each metal type will receive paint A and the other half will receive paint B. The adhesion of the paints was measured, and the measures were compared. How many experimental units are in the experiment?
30
Matt wants to investigate the opinions of young adults in the country, ages 18 years to 25 years, about time spent playing video games. He plans to administer a survey to a sample of people. Which of the following samples is most likely to generalize to his population of interest?
A nationwide sample of people ages 18 to 25
A pottery school wants to study whether the glaze of stoneware bowls is affected by the temperature used to harden the bowls. The study will use 3 different types of clay because glaze can affect different clay in different ways. Eight bowls will be made with each clay type for a total of 24 bowls, and 4 different temperatures will be used. What is the best design to use for the study?
A randomized block design. Randomly assign temperatures so that 2 bowls of each clay type are glazed at each temperature.
The owner of a plant nursery will conduct a study to investigate whether a new fertilizer is more effective than an older fertilizer in helping the growth of young tomato seedlings. The owner selects a simple random sample of 50 young tomato seedlings from all the young tomato seedlings in the nursery. Half of the selected seedlings will be randomly assigned to receive the new fertilizer, and the remaining seedlings will receive the older fertilizer. The growth of the seedlings will be recorded for the next month. What is the main reason in the study for selecting a simple random sample from the population?
A simple random sample selected from the population allows the results to be generalized to the population.
Observational Study
A study where data is gathered by simply observing, no treatments offered -Retrospective: Looking into the past to observe data -Prospective: Identifying subjects in advance and collecting data as events unfold
Placebo
A treatment where the subject thinks they are getting treatment, but they are not
Factor
A variable whose levels are manipulated by the experimenter
A candidate for mayor of Dallas calls 1,000 people chosen at random from the city telephone directory; 850 of them respond. What are the sampling frame and the sample in this example? A. SF: the telephone directory. S: the 850 people who respond B. SF: the telephone directory. S: the 1,000 people who are called C. SF: the 1,000 people who are called. S: the 850 people who respond D. SF: all Dallas residents. S: the 1,000 people who are called E. SF: all Dallas residnts. S: the 850 people who respond
A. SF: the telephone directory. S: the 850 people who respond
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. 10 bands from the Brand A box are placed in a freezer for 2 hours and 10 bands from Brand B are kept at room temperature. The amount of stretch before breakage is measure 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? A. no, because the means are not proper statistics for comparison B. no, because more than 2 bands should be used C. no, because more temperatures should be used D. no, because temperature is confounded with brand E. yes
D. no, because temperature is confounded with brand
A consumer product agency tests oles per gallon for a sample of automobiles using each of 4 different octanes of gasoline. Which of the following is true? A. there are 4 explanatory variables and 1 response variable B. there is 1 explanatory variable with 4 levels of response C. milers per gallon is the only explanatory variable, but there are 4 response variables corresponding to the different octanes D. there are 4 levels of a single explanatory variable E. none of the above are true
D. there are 4 levels of a single explanatory variable
A researcher randomly selected 30 people to participate in a study to investigate which of two materials, A or B, used in the heels of sneakers will last longer. The researcher is considering two design types for the study. I. Design 1: Randomly assign 15 participants to wear sneakers with material A on their left feet and material B on their right feet. The remaining participants will wear sneakers with material B on their left feet and material A on their right feet. II. Design 2: Randomly assign 15 participants to wear sneakers with material A on both feet and the remaining participants to wear sneakers with material B on both feet. Which of the following best describes each design?
Design 1 is a matched pairs design, and design 2 is a completely randomized design.
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? A. biased random sample B. nonrandom sample C. simple random sample D. stratified random sample E. cluster random sample
E. cluster random sample
Which of the following are true statements? 1. under-coverage bias can be overcome by greatly increasing the sample size 2. well-designed probability samples always eliminate bias 3. response bias results only from the wording of survey questions A. 1 only B. 2 only C. 3 only D. 2 and 3 E. none of these
E. none of these
The distribution of wait times for customers at a certain department of motor vehicles in a large city is skewed to the right with mean 23 minutes and standard deviation 11 minutes. A random sample of 50 customer wait times will be selected. Let x¯W represent the sample mean wait time, in minutes. Which of the following is the best interpretation of P(x¯W>25)≈0.10 ?
For a random sample of 50 customer wait times, the probability that the sample mean customer wait time will be greater than 25 minutes is approximately 0.10.
Sampling Bias
Sampling methods that, by their nature, tend to over- or underemphasize same characteristics of the population
A researcher conducted a study investigating the effect of computer screen time on a person's amount of REM sleep. The researcher randomly assigned 100 people into four groups. The first group was given 2 hours of computer screen time each day, the second group was given 4 hours each day, the third group was given 6 hours each day, and the fourth group was given 8 hours each day. The study was conducted for one week, and the amount of REM sleep for each person was measured. What is the explanatory variable in the study?
The amount of computer screen time
Population
The entire group of individuals or instances about whom we hope to learn
Census
The entire population is examined in hopes of learning in hopes of learning about the population
A professor at a large university plans to conduct a study to compare the effect of online texts versus regular printed texts on student learning. If the findings are to be generalized to all students at the university, which of the following must be part of the design?
The students in the study should be a random sample from the population of students at the university.
control group
a group created the provide a basis for comparison usually either an old or placebo treatment
sampling frame
a list of individuals from whom the sample is drawn
population parameter
a numerically valued attribute of a model for a population
convenience sampling
a poor way to collect a sample - do what is convenient for the surveyor, data is usually very biased
systematic sample
a sample drawn by selecting individuals systematically from a sampling frame
systematic sample
a sample is drawn from the population by following a systematic plan to give every object in the population an equal chance to be chosen but all possible groups can not be formed
undercoverage
a sampling scheme that biases the sample in a way that gives a part of the population less representation than it has in the population
factor
a variable whose levels are controlled by the experimenter
factor
a variable whose levels are controlled by the experimenter to discover its effects on the subjects
a simple random sample
is a specific type of probability sampling that gives every individual an equal chance to be chosen and also gives every possible sample an equal chance to be chosen to choose an SRS we first assign numerical label to every individual in the population and then select labels at random using some random mechanism
Advantage of adding a control group
it will reduce variability of the responses, makes it easier to detect differences among treatment groups
Nonresponse bias
large fraction os those samples fails to respond, can recover if you can identify and go after them
With a voluntary sample, many who have stronger negative/positive opinions are left out
negative
Name the sampling strategy: There are 4 employee classifications: supervisors, full-time clerks, part-time clerks, and maintenance staff. Randomly select 10 people from each category.
stratified sample
sample size
the number of individuals in a sample
treatment
the process, intervention, or other controlled circumstance applied to randomly assigned experimental units
A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2 ?
2.7−4.2=−1.52.7−4.2=−1.5
The manager of a public swimming pool wants to compare the effectiveness of 2 laundry detergents, detergent A and detergent B, in cleaning the towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine contains 20 towels, the manager flips a coin to determine whether detergent A or detergent B will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. Which of the following best describes the manager's study? A. a completely randomized design B. a randomized block design with detergent A and detergent B as blocks C. a randomizes block design with the washing machine as the block D. a matched-pairs design with detergent A and detergent B as the pair E. an observational study
A. a completely randomized design
Suppose that 30% of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of 5 randomly selected subscribers watches the shopping channel at least once a week. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation? A. assign 0,1,2 as watching the shopping channel at least once a week and 3,4,5,6,7,8, and 9 as not watching B. assign 1,2,3,4 as watching the shopping channel at least once a week and 4,5,6,7,8, and 9 as not watching C. assign 1,2,3,4,5 as watching the shopping channel at least once a week and 6,7,8,9 and 0 as not watching D. assign 0 as watching the shopping channel at least once a week and 1,2,3,4 and 5 as not watching; ignore digits 6,7,8, and 9 E. assign 3 as watching the shopping channel at least once a week and 0,1;2,4,5,6,7,8 and 9 as not watching
A. assign 0,1,2 as watching the shopping channel at least once a week and 3,4,5,6,7,8, and 9 as not watching
An important advantage of using a randomized block design in an experiment is: A. it controls for the effects of factors that may confound your results B. eliminating of all possible lurking variables that may confound the effect of the treatment C. reducing bias associated with using multiple interviewers D. collecting information from the subjects before and after the administration of a treatment E. all of above
A. it controls for the effects of factors that may confound your results
A researcher is testing the effect of a new fertilizer on crop growth. He marks 30 plots in a field, splits the plots in half, and randomly assigns the new fertilizer to one half of the plot and the old fertilizer to the other half. After 4 weeks, he measures the crop yield and compares the effects of the two fertilizers. This design is an example of A. matched pairs experiment B. completely randomized comparative experiment C. cluster experiment D. double-blind experiment E. this is not an experiment
A. matched pairs experiment
Which of the following statements is true? A. nonresponse can cause bias in surveys because nonrespondents may have different opinions than people who responded B. bias arising from undercoverage can be compensated for by increasing sample size C. stratified random sampling is often employed to reduce the impact of response bias D. people's responses to survey questions tend not to be influenced by the age, race, or sex of the interviewer E. sophisticated statistical methods can always correct the results if the population you are sampling from is different from the population of interest, for example, due to undercoverage
A. nonresponse can cause bias in surveys because nonrespondents may have different opinions than people who responded
A member of Congress wants to know what his constituents think of proposed legislation on health insurance. His staff reports that 228 letters have been received on the subject, of which 193 opposed the legislation. What is the population in this situation? A. the constituents B. the 228 letters received C. the 193 opposing the legislation D. Congress E. none of the above
A. the constituents
A probability sample is any sample in which A. every member of the population has the same chance of being selected B. every member of the population has a known, nonzero chance of being selected C. the population is first divided into groups of similar individuals and then a separate SRS is selected from each group and combined to form the full sample D. all collections of members of the population have the same chance of being selected
B. every member of the population has a known, nonzero chance of being selected
The most important advantage of experiments over observational studies is that A. experiments are usually easier to carry out B. experiments can give better evidence of causation C. confounding cannot happen in experiments D. an observational study cannot have a response variable E. observational studies cannot use random samples
B. experiments can give better evidence of causation
In the late 1990's, Scotland was considering independence from England. An opinion poll showed that 51% of Scots favor "independence." Another poll taken at the same time showed that only 34% favored being "separate" from England. The reason these differ by so much is that A. samples will usually differ just by chance due to random sampling B. the wording of questions has a big effect on poll results C. more follow-up efforts reduced the nonresponse rate of the second poll D. the sample sizes are different, so the margins of error are different E. the second poll suffered from undercoverage
B. the wording of questions has a big effect on poll results
What is the one reason for using random allocation to assign units to treatments in an experiment? A. to produce the placebo effect B. to produce experimental groups that are similar C. to eliminate lack of realism D. to produce the blocks in a block design
B. to produce experimental groups that are similar
The distribution of height for a certain population of women is approximately normal with mean 65 inches and standard deviation 3.5 inches. Consider two different random samples taken from the population, one of size 5 and one of size 85. Which of the following is true about the sampling distributions of the sample mean for the two sample sizes?
Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.
When the effects of 2 variables in an experiment cannot be separates and hence we cannot say which is responsible for the observed responses, we say the variables are what? A. dependent B. factors C. confounded D. blocked
C. confounded
If changes in a response variable are due to the effects of the explanatory variable as well as the effects of lurking variables, and we cannot distinguish between these effects, we are said to have A. a cause and effect relation between the explanatory and response variable B. a placebo effect C. confounding D. correlation E. extrapolated
C. confounding
A researcher identifies a sample of teenagers and chooses 2 males, both 16, from lower-income families. She randomly assigns one of the males to be in an intensive tutoring course; she places the second male in a standard classroom. She continues doing this with pairs of males and females. This is an example of A. blocking based on gender B. match pairs on responses before and after the tutoring session C. matched pairs on gender, age, and income status for random assignment D. completely randomized teenagers to treatment and control groups E. blocking teenagers based on gender, age, and income status
C. matched pairs on gender, age, and income status for random assignment
A new cough medicine was given to a group of 25 subjects who had a cough due to the common cold. 30 minutes after taking the new medicine, 20 of the subjects reported that their coughs had disappeared. From this information you conclude A. that the remedy is effective for the treatment of coughs B. nothing, because the sample size is too small C. nothing, because there is no control group for comparison D. that the new treatment is better than the old medicine E. that the remedy is not effective for the treatment of coughs
C. nothing, because there is no control group for comparison
At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a SD of 12. The scores on the calculus final are also approximately normally distributed with a mean of 80 and a SD 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? A. the student did better in chemistry B. the student did better in calculus C. the student did equally well in each course D. there is no basis for comparison E. there is not enough information, because the number of students in each class is not known
C. the student did equally well in each course
For a certain experiment you have 8 subjects, of which 4 are female and 4 are male. The names of the subjects are listed below: Males: atwater, bacon, chu, diaz Females: johnson, king, liu, moore There are 2 treatments, A and B. If a randomized block design is used, with the subjects blocked by their gender, which of the following is not a possible group of subjects who receive treatment A? A. atwater, chu, king, liu B. bacon, chu, liu, moore C. atwater, diaz, liu, king D. atwater, bacon, chu, johnson E. atwater, bacon, johnson, king
D. atwater, bacon, chu, johnson
A study of existing records of 27,000 automobile accidents involving children in Michigan found that about 10% of children who were wearing a seatbelt (group SB) were injured and that about 15% of children who were not wearing a seatbelt (group NSB) were injured. Which of the following statements should NOT be included in a summary report about this study? A. driver behavior may be a potential confounding factor B. the child's location in the car may be a potential confounding factor C. this study was not an experiment, and cause and effect inferences are not warranted D. this study demonstrates clearly that seat belts save children from injury E. seatbelt usage is associated with child injury during automobile accidents involving children
D. this study demonstrates clearly that seat belts save children from injury
A cause and effect relationship between 2 variables can best de determined from which of the following? A. a survey conducted using an SRS of individuals B. a survey conducted using a stratified random sample of individuals C. when the 2 variables have a correlation coefficient near 1 or -1 D. an observational study where the observational units are chosen randomly E. a controlled experiment where the observational units are assigned randomly
E. a controlled experiment where the observational units are assigned randomly
The essential difference between an experiment and an observational study is that A. observational studies may have confounded variables, but experiments never do B. in an experiment, people must give their informed consent before being allowed to participate C. observational studies are always biased D. observational studies cannot have response variables E. an experiment imposes treatments on the subjects, but an observational study does not
E. an experiment imposes treatments on the subjects, but an observational study does not
In which of the following situations would it be most difficult to use a census? A. to determine what proportion of licensed bicycles on a university campus have lights B. to determine what proportion of students in a high school supported wearing uniforms C. to determine what proportion of registered students enrolled in a college employed more than 20 hours a week D. to determine what proportion of single-family dwellings in a small town have 2-car garages E. to determine what proportion of fish in Lake Michigan are bass
E. to determine what proportion of fish in Lake Michigan are bass
Name the sampling strategy: Choose the 4th person that arrives to work for each shift.
systematic sample
Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility vehicles. In this study,
(a) gas mileage is a response variable, and you expect to find a negative association
In the course decribed in #2, Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?
(b) 2.0
The president of a small company needs to collect data on the educational background of all 20 of the company's employees. Which of the following is the best method to use for data collection?
A census
Control Group
A group of subjects in a study who take the placebo
Sampling frame
A list of individuals from which the sample is drawn
Voluntary response
A sample where respondents can choose whether or not to respond to a survey
Experiment
A study where data is gathered by observing a situation where one or more treatments were provided
Sample
A subset of a population examining in hope of learning about the population
Randomized block design
An experiment when subjects are randomly assigned treatments within each block
The distribution of the number of siblings for students at a large high school is skewed to the right with mean 1.8 siblings and standard deviation 0.7 sibling. A random sample of 100 students from the high school will be selected, and the mean number of siblings in the sample will be calculated. Which of the following describes the sampling distribution of the sample mean for samples of size 100 ?
Approximately normal with standard deviation less than 0.7 sibling
To investigate the effectiveness of an herbal medication for pain relief, a researcher randomly selected 80 patients who were undergoing physical therapy while recovering from an injury. Of the patients, 40 had knee injuries, 16 had arm injuries, and 24 had foot injuries. The researcher will use two treatments for the investigation: the herbal medication and a standard medication. After the patients are on the medication for two weeks, the amount of pain reduction will be measured for each patient. Which of the following best describes why a randomized block design is appropriate for the investigation?
Blocking on injury type will help to separate natural variability from differences due to injury type.
To estimate the size of a typical housing unit in a certain town, a sociologist plans to use a cluster sampling method to gather data. Which of the following describes a cluster sampling method?
Divide the town into nonoverlapping regions. Randomly select from the nonoverlapping regions, and select all housing units in those regions.
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
E) Minimizing the sum of the squares of the residuals
The Physician's 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 11,0000 physicians took an aspiring every other day, while a control group took a placebo. After several years, it was determined that the physicians in the group that took aspiring 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 aspiring every other day? 1. the study included only physicians, and different results may occur in other occupations 2. the study included only males and there may be different results for females 3. although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health A. 1 only B. 2 only C. 3 only D. 2 and 3 only E. 1, 2, and 3
E. 1, 2, and 3
A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true? A. the bank should not use the data from this survey because this is an observational study B. the bank can use the result of this survey to prove that woking for the bank causes employees to participate in volunteer activities C. the bank did not select a random sample of employees, so the survey will not provide the bank with useful information D. the bank would have to use the survey to construct a confidence interval in order to estimate the proportion of employees who participate in volunteer activities E. the bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all employees.
E. the bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all employees.
The two graduates with the greatest GPA from each of 14 randomly selected law schools were recruited to investigate a new method of preparation for a law exam. For each school, one student was randomly assigned to prepare using the standard method and the other student was assigned to prepare using the new method. At the end of the preparation, all 28 students were given the same exam, and their scores were recorded. Which of the following best describes why a matched-pairs design is an appropriate design for the investigation?
Each law school served as a block, and the graduates were paired within each law school and randomly assigned to one of the two methods.
Diane wanted to demonstrate which pruning technique was best for controlling the growth of certain types of shrubs. She selected ten shrubs of the same type and randomly assigned each one to receive one of ten different pruning methods. Two weeks after pruning, she measured the regrowth, in inches, of the shrubs; the pruning method that minimized regrowth was recommended as the best method. Which of the following best describes why this is not a well-designed experiment?
Each pruning method was used on only one shrub.
Trial
Each time a response is obtained from a specific question
Simulation
Models a real world situation by using random digits to model simple random occurrences whose outcomes may not be equally likely
Child psychologists study the time, in months, that it takes for infant boys and girls to say their first words. For a certain population, the distributions of time for both populations have the same mean and have the same standard deviation, μ=8 months and σ=1.4 months. Two independent random samples of infant boys and girls were taken, and the time it took for the infants in each sample to say their first words was recorded. The summary statistics for the number of months are shown in the following table. Riley, a child psychologist, claims that for all samples of size 40 from the population of infant boys and all samples of size 40 of newborn girls, the mean of the sampling distribution of the difference in sample means (boys minus girls) is 0.2 month. Is Riley correct?
No, the mean is 8−8=0 months.
Stratified
Organize the sampling frame into two or more groups and randomly select amounts from each group
Cluster
Organize the sampling frame into two or more groups and survey everyone in those groups
A survey will be sent to dog owners to investigate their opinions on multiple topics. Which of the following questions on the survey is most likely to contribute to question-wording bias?
Should responsible dog owners purchase pet insurance?
Matching
Subjects who are similar in ways not under study may be matched and then compared with each other on the variables of interest
The distribution of the commute times for the employees at a large company has mean 22.4 minutes and standard deviation 6.8 minutes. A random sample of n employees will be selected and their commute times will be recorded. What is true about the sampling distribution of the sample mean as n increases from 2 to 10 ?
The mean does not change, and the variance decreases.
The mean age of the employees at a large corporation is 35.2 years, and the standard deviation is 9.5 years. A random sample of 4 employees will be selected. What are the mean and standard deviation of the sampling distribution of the sample mean for samples of size 4 ?
The mean is 35.2, and the standard deviation is 9.5/2.
A sports magazine reports that the mean number of hot dogs sold by hot dog vendors at a certain sporting event is equal to 150. A random sample of 50 hot dog vendors was selected, and the mean number of hot dogs sold by the vendors at the sporting event was 140. For samples of size 50, which of the following is true about the sampling distribution of the sample mean number of hot dogs sold by hot dog vendors at the sporting event?
The mean of the sampling distribution of the sample mean is 150 hot dogs.
For a weekly town council meeting in a certain town, the distribution of the duration of the meeting is approximately normal with mean 53 minutes and standard deviation 2.5 minutes. For a weekly arts council meeting in the same town, the distribution of the duration of the meeting is approximately normal with mean 56 minutes and standard deviation 5.1 minutes. Let x¯1 represent the average duration, in minutes, of 10 randomly selected town council meetings, and let x¯2 represent the average duration, in minutes, of 10 randomly selected arts council meetings. Which of the following is the best reason why the sampling distribution of x¯1−x¯2 can be modeled by a normal distribution?
The population distributions are approximately normal.
Level
The specific values that the experimenter chooses a factor
A certain store has 3,000 employees working at its main location in a city and 100 employees working at a smaller location outside the city. The store manager will select a sample of 50 employees from all the employees to ask their opinions about extending store hours during the holidays. What is the advantage of selecting a stratified random sample, with location as strata, instead of a simple random sample?
The stratified sample assures that the opinions of employees from both locations will be represented.
A teacher at a culinary arts school will conduct an experiment to investigate which of three methods of instruction works best in teaching students how to make a good pie crust. Each student in a group of 60 students will be randomly assigned to one of three methods: in-person demonstration by the instructor, watching a video, and reading a recipe. The students will be assigned so that each method will have 20 students. Each pie crust made will be judged on its taste and texture. What are the treatments of the experiment?
The three methods of instruction
Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment?
The treatments (new menu item) were not randomly assigned to the students.
A researcher conducted an experiment to investigate the effectiveness of a medicated lotion in treating a skin irritation. A group of 80 people with a history of skin irritation volunteered for the study. Of the 80 people, 40 were randomly assigned the medicated lotion, and the remaining 40 were given a nonmedicated lotion. At the end of one month, the skin irritation had cleared for 36 people (90 percent) using the medicated lotion and 16 people (40 percent) using the nonmedicated lotion. Analysis of the results showed the difference was statistically significant. What can be concluded from the experiment?
There is enough evidence to conclude that the medicated lotion is more effective than the nonmedicated lotion in treating the skin irritation.
A company famous for its nacho-flavored corn chips has developed two new formulas, A and B, which they hope their customers will like even more than the original formula. To determine whether customers prefer one of the new formulas over the current nacho flavoring, a sample of 50 customers is obtained. Each customer tastes both formula A and formula B in a randomly assigned order and indicates which one they prefer more. Which of the following best describes this study?
This study is not well designed because formulas A and B are not compared with the original formula.
A scientist studying soil acidity collected soil samples from a plot of land with a stream running through it. The soil samples came from land located on only one side of the stream. What is the potential source of bias that might result from the sampling method?
Undercoverage bias
sample
a representative subset of a population, examined in hope of learning about the population
representative
a sample is this if the statistics computed from it accurately reflect the corresponding population parameters
cluster sample
a sampling design in which entire groups are chosen at random
stratified random sample
a sampling design in which the population is divided into several subpopulations, and random samples are then drawn from each stratum
observational study
a study based on data in which no manipulation of factors has been employed
observational study
a study based on data where no manipulation of factors has been employed, we simply observe what has or will happen
sample survey
a study that asks questions of a sample drawn from some population in the hope of learning something about the entire population
experiment
a study where there is a definite random assignment of subjects to treatments
retrospective study
a study where we collect data from events that have happened in the past
placebo
a treatment known to have no effect, administered so that all groups experience the same conditions
response (in regards to experiment)
a variable whose values are compared across different treatments
simple random sample
abbreviated SRS, this requires that every item in the population has an equal chance to be chosen and that every possible combination of items has an equal chance to exist. No grouping can be involved.
completely randomized design
all experimental units have an equal chance of receiving any treatment
experiment
and deliberately imposes some treatment on the individuals in order to serve the responses this is good for determining cause and effect
response bias
anything in a survey design that influences response
response bias
anything in the survey design that influences the responses from the sample
nonresponse bias
bias introduced to a sample when a large fraction of those sampled fails to respond
voluntary response bias
bias introduced to a sample when individuals can choose on their own whether to participate in the sample
Double-blind stufy
both subjects and evaluators are unaware
A confounding variable can/cannot be distinguished
cannot
principles of experimental design
control, randomization, and replicate
Randomizes block design
experimental design that decreases the variability within the samples
cluster sample
is another type of probability sampling in which the population is put into clusters usually based on location and then clusters of individuals are chosen at random the difference here is we are not choosing one individual at a time but an entire cluster at a time
judgment sample
is one in which an expert chooses those individuals that they feel best represent the entire population
experiment
manipulates factor levels to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject groups across treatment levels
sample statistics
mathematical measures taken from a sample of the population of interest like the sample mean and sample standard deviation
population parameter
mathematical measures taken from the entire population like the population mean and standard deviation
Blocking
reduces variability within the treatment groups
multistage sample
sampling schemes that combine several sampling methods
matched
subjects who are similar in ways not under study may be ____ and then compared with each other on the variables of interest
control group
the experimental units assigned to a baseline treatment level, typically either the default treatment, which is well understood, or a null, placebo treatment
randomization
the random selection of subjects used to reduce bias in either surveys or experiments
level
the specific values that the experimenter chooses for a factor
placebo effect
the tendency of many human subjects (often 20% or more of experiment subjects) to show a response even when administered a placebo
confounding variable
the variable that is related to both group membership in the response variable of interest
wording effects
the wording of questions is the most important influence on answers given to a sample survey wording that is confusing can often lead to answers that don't represent the true feelings
non response
this occurs when an individual selected as part of the sample can't be contacted or does not want to cooperate
under coverage selection bias
this occurs when some groups in the population are left out of the process of choosing the sample
response bias
this refers to the fact that often answers to questions do not always represent the true feeling opinions ect. a of the respondent
matched design
when our data values are not independent of one another and are related somehow to one subject - it is a form of blocking
bias
when sampling methods either over or under emphasize some characteristic of the population
single blind
when the subjects in an experiment do not know if they are in the treatment or control group
Suppose that the night before a national election, the host of a radio show asked callers to call his program and indicate which of the candidates they would vote for. At the end of the program, the radio show host indicated that, based on his survey, a certain candidate would likely win. However, on the election day, the candidate lost. Which of the following is the most likely explanation for why the radio show's survey was wrong? A. the survey was voluntary, and only those who wanted to participate did B. the question to the callers was slanted, producing incorrect results C. a large number of callers lied in their responses D. the survey was accurate, but many people changed their minds when they voted E. the sample size was too small
A. the survey was voluntary, and only those who wanted to participate did
A polling form is interested in surveying a representative sample of registered voters in the US. The form has automated its sampling so that random phone numbers within the US are called. Each time a number is called, the procedure below is followed. if there is no response or if an answering machine is reached, another number is automatically called if a person answers, a survey worker verifies that the person is at least 18 years of age if the person is not at least 18 years of age, no response is recorded, and another number is called if the person is at least 18 years of age, that person is surveyed Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used? A. registered voters with children under the age of 18 years may be underrepresented in the sample B. registered voters with unlisted telephone numbers may be underrepresented in the sample C. registered voters who have more than one telephone number may be overrepresented in the sample D. registered voters who live in households consisting of more than one voter may be underrepresented E. people who are not registered to vote may bias the sample results
B. registered voters with unlisted telephone numbers may be underrepresented in the sample
A researcher wishes to test a new drug developed to treat hypertension (high blood pressure). A group of 40 hypertensive men and 60 hypertensive women is to be used. The experimenter randomly assigns 20 of the men and 30 of the women to the placebo and assigns the rest to the treatment. The major reason for separate assignment for men and women is that A. it is a large study with 100 subjects B. the new drug may affect men and women differently C. the new drug may affect hypertensive and non-hypertensive people differently D. this design uses matched pairs to detect the new-drug effect E. there must be an equal number of subjects in both the placebo group and the treatment group
B. the new drug may affect men and women differently
A researcher is testing a company's new stain remover. He has contracted with 40 families who have agreed to test the product. He randomly assigns 20 families to the group that will use the new stain remover and 20 to the group that will use the company's current product. The most important reason for this random assignment is that A. randomization makes the analysis easier since the data can be collected and entered into the computer in any order B. randomization eliminates the impact of any confounding variables C. randomization is a good way to create 2 groups of 20 families that are as similar as possible, except for the treatments they receive D. randomization ensures that the study is double-blind E. randomization reduces the impact of outliers
C. randomization is a good way to create 2 groups of 20 families that are as similar as possible, except for the treatments they receive
The results of an experiment are said to be statistically significant if what? A. they are important to statisticians, regardless of their importance to the investigators B. both researchers and statisticians agree the results are meaningful and important C. the observed effect is too large to attribute plausible to chance D. they support the findings of previous, similar study
C. the observed effect is too large to attribute plausible to chance
A movie studio runs an experiment in order to decide which of 2 previews to use for its advertising campaign for an upcoming movie. One preview features the movie's romantic scenes and is expected to appeal more to women. The other preview features the movie's action scenes and is expected to appeal more to men. 16 subjects take part in this experiment, 8 women and 8 men. After viewing one of the previews, each person will rate how much he or she wants to see the movie. Which of the following best describes how blocking should be used in this experiment? A. use blocking, with half the mean and half the women in each block B. do not block, because the preview that is chosen will have to be shown to audiences consisting of both men and women C. do not block, because the response will be confounded with gender D. use blocking, with the men in one block and the women in the other E. do not block, because the number of subjects is too small
D. use blocking, with the men in one block and the women in the other
A researcher planning a survey of heads of households in New York has census lists for each of the 62 counties in the state. The procedure will be to obtain a simple random sample of heads of households from each of the counties rather than grouping all the census lists together and obtaining a sample from the entire group. Which of the following is a true statement about the resulting stratified sample? 1. it is more susceptible to bias than would be a simple random sample 2. it is easier and more cost effective than a simple random sample 3. it gives comparative information that a simple random sample wouldn't give A. 1 and 2 B. 1 and 3 C. 2 and 3 D. 1, 2, and 3 E. none of the above gives the complete set of true responses
E. none of the above gives the complete set of true responses
bias
any systematic failure of a sampling method to represent its population; common errors are voluntary response, undercoverage, nonresponse ____, and response ____
Response bias
anything in the design that influenced responses, interview behavior, wording of the question
component
model used in simulation
Random digits are truly _____
random, if another list of random digits is used to select the sample, the results obtained with the list actually used would be just as likely to be selected as any other set of 3 names