STAT Chapter 1
any item or quantity that can vary or take on different values
variable
the items or quantities that the study seeks to measure
variables of interest
subset of the population from which data are actually obtained
sample
A margin of error is used to describe the range of values likely to contain a population parameter and is added to and subtracted from a
sample statistic
A pollster conducts a research project about how adult Chinese pay their bills. She posts her survey online and obtains 45 responses. Is the sample likely to be representative of the population? Yes No
No
The sample is chosen for convenience rather than by a more sophisticated procedure.
convenience sampling
occurs when a researcher or experimenter somehow influences subjects through such factors as facial expression, tone of voice, or attitude
experimenter effect
In a Gallup poll of 1 comma 073 randomly selected American sportsmen, 89% said that cloning of humans should not be allowed. Identify the sample, population, and sampling method. Then comment on whether you think it is likely that the sample is representative of the population. Identify the sample. Choose the correct answer below. Identify the sampling method. Choose the correct answer below. A: Convenience B: Systematic C:Random
C
What is the fourth step of a statistical study?
Use the sample statistics to make inference about the population
a sample statistic is
a number that describes a characteristic of a sample
a population parameter is
a number that describes a characteristic of the population
et up to collect data in the future from groups that share common factors
prospective or longitudinal study
actual measurements or observations collected from the sample
raw data
sample in which the relevant characteristics of the sample members are generally the same as the characteristics of the population
representative sample
variable that responds to change in the explanatory variable
response variable
raw data are
the individual measurements collected
A margin of error is used to describe the range of values likely to contain a
population parameter
specific numbers describing characteristics of the population
population parameters
uses data from the past, such as official records or past interviews
retrospective or case control study
numbers describing characteristics of the sample found by consolidating or summarizing the raw data.
sample statistics
Convenience sampling can cause possible
sampling biases
group of subjects who receive the treatment being tested
treatment group
The margin of error is usually defined to give a __ percent confidence interval
95
What does the 95% confidence interval mean?
95% of samples the size used in the study would contain the actual population parameter
What is the second step in a statistical study?
Choose a representative sample from the population.
What is the first step in a statistical study?
State the goal of the study
We find the confidence interval by _______ ___ ______ the margin of error from the sample statistic obtained in the study
adding and subtracting
A statistical study suffers from ____ if its design or conduct tends to favor certain results.
bias
collection of data from every member of a population
census
involves the selection of all members in randomly selected groups. Usually divided into more abstract groups, such as majors or sports or brands.
cluster sampling
The population is the
complete set of people or things being studied
A margin of error is used to describe the range of values likely to contain a population parameter and is added to and subtracted from a sample statistic to establish a
confidence interval
A study suffers from confounding if the effects of different variables are mixed, so we cannot determine the specific effects of the variables of interest. The variables that lead to the confusion are called
confounding variables
group of subjects who do not receive the treatment being tested
control group
neither the participants nor any experimenters know who belongs to the treatment group and who belongs to the control group
double-blind
researchers observe or measure characteristics of the subjects but do not attempt to influence or modify these characteristics
observational study
lacks the active ingredients of a treatment being tested in a study but looks or feels like the treatment so that participants cannot distinguish whether they are receiving the placebo or the real treatment.
placebo
refers to the situation in which patients improve simply because they believe they are receiving a useful treatment.
placebo effect
in a statistical study is the complete set of people or thing being studied
population
every possible sample of a particular size has an equal chance of being selected.
simple random sampling
participants do not know whether they are members of the treatment group or members of the control group, but the experimenters do know.
single-blind
A marketing expert for a particular chain of restaurants is planning a survey in which 484 people will be randomly selected from each age group: 10-19, 20-29, and so on. Is the procedure likely to yield a representative sample or a biased sample? Explain why. A: The procedure is likely to yield a representative sample because it covers every age group. B: The procedure is likely to be biased because people from those age groups are not evenly distributed throughout the population. C: The procedure is likely to be representative because 484 people from each age group form a large sample size. D: The procedure is likely to yield a biased sample because younger people don't know what they want and should be studied separately.
B
What are two ways to diminish the possibilities of confounding variables?
selecting groups at random and using large groups
a sample is the
set of people or things from which the data are obtained
science of collecting, organizing, and interpreting data and/or the data (numbers or other pieces of information) that describe or summarize something.
statistics
involves randomly selecting members from each stratum. Usually divided into more universal groups, such as gender and age.
stratified sampling
in a statistical study is used to describe the range of values, or confidence interval, likely to contain the population parameter
margin of error
The confidence interval is used to estimate a
population parameter
Define response variable. Select the correct answer below. A: Any item or quantity that causes a response in another value B: A variable that responds to changes in the explanatory variable C: A variable that may explain or cause the effect D: Any item or quantity that has an unknown value
B
Determine whether a census is practical in the situation described below. Explain your reasoning. A student wants to determine the mean IQ of all female students at all colleges in a country. Choose the correct answer below. A: A census is practical. The population consists of a small number of female students at all colleges in a country, and it easy to obtain their IQs. B: A census is not practical. The population consists of a large number of female students at all colleges in a country, and it is not easy to obtain their IQs. C: A census is practical. The population consists of a large number of female students at all colleges in a country, and it is not easy to obtain their IQs. D: A census is not practical. The population consists of a small number of female students at all colleges in a country, and it easy to obtain their IQs.
B
Determine whether the following study is an observational study, an experiment, or a meta-analysis, and explain your choice. Upper A census of a statistics class is conducted in which students are asked whether they prefer texting or traditional calling. Choose the correct answer below. A: The study is a meta-analysis because an analysis of the data was used to determine effectiveness. B: The study is an observational study because there was no attempt to influence the results. C: The study is a meta-analysis because the study was done on a group. D: The study is an experiment because there is a treatment group and a control group. E: The study is an experiment because a hypothesis is tested. F: The study is an observational study because the data were collected all at once.
B
How are the explanatory and response variables related to each other? A: The response variable responds to any confounding caused by the explanatory variable. B: The explanatory variable may cause the response variable to change. C: The response variable is usually static while the explanatory variable is varied. D: The explanatory variable explains any response caused by the response variable.
B
The following claim might be addressed in an experiment: A company is developing a new plastic for remote control boats, and it is claimed that the new plastic lasts significantly longer than those currently in use. What would he choose as the treatment group? Select the correct answer below. A: Remote control boats that use the new plastic, because it is better B: Remote control boats, because they are what the treatment is applied to C: Remote control boats that use the new plastic, because the study is looking for an effect from the new plastic D: Anything that uses a plastic, because that is what is being varied E: Anything that uses the new plastic, because the study is looking for the effect of using the new plastic F: Anything that uses a current plastic, because the study is looking for the difference from using a current plastic
C
A researcher plans to investigate the belief that people are more comfortable in the summer sun when they wear clothing with light colors instead of clothing with dark colors. Does it make sense to use a double-blind experiment in this case? Is it easy to implement blinding in this case? Explain. A: No, because the color of clothing that a person is wearing is usually not obvious. The study would have to be carefully designed so that both the subject and the researchers could discern the shade of the participants' clothing. B: Yes, because the color of clothing that a person is wearing is usually quite obvious. The study would have to be carefully designed so that neither the subject nor the researchers could discern the shade of the participants' clothing. C: Yes, because the color of clothing that a person is wearing is usually not obvious. The study would have to be carefully designed so that both the subject and the researchers could discern the shade of the participants' clothing. D: No, because the color of clothing that a person is wearing is usually quite obvious. The study would have to be carefully designed so that neither the subject nor the researchers could discern the shade of the participants' clothing.
D
A college dean obtains an alphabetical list of all full-time students at her college and she selects every 35th name on that list and surveys those students to find the amount of student debt incurred by each of them. She uses the results to estimate the average (mean) amount of student debt incurred by college students in the United States. What type of sampling is used? A: Systematic sampling B: Your answer is correct. C: Convenience sampling D: Simple random sampling E: Stratified sampling F: Cluster sampling
A
A marketing expert for a particular chain of restaurants is planning a survey in which 484 people will be randomly selected from each age group: 10-19, 20-29, and so on. What type of sampling is used? A: Stratified sampling B: Systematic sampling C: Cluster sampling D: Simple random sampling E: Convenience sampling
A
Based on a recent survey of adults in 60 comma 000 households, a labor department reported an unemployment rate of 4.6%. The margin of error was 0.3 percentage point. a. Based on the given information, state what you think was the goal of the study. Identify a possible population and the population parameter of interest. What is the goal of this study? Choose the correct answer below. A. To determine how many adults in each household are unemployed B. To determine if adults can be unemployed and keep their households C. To determine the percentage of adults who are unemployed Your answer is correct.D. To determine what effect unemployment has on household status Identify a possible population. Choose the correct answer below.
A
Briefly describe the sample, raw data, and sample statistic for the study. What is the sample for this study? Choose the correct answer below. A: The sample of adults selected for the survey B: 4.6% of all adults C: The complete set of all adults D: 4.6% of the adults selected for the survey
A
Determine whether a census is practical in the situation described. Explain your reasoning. You want to determine the mean height of all basketball players in a country. Choose the correct answer below. A: A census is not practical. The population consists of the large number of players in a country, and it not easy to obtain their heights. B: A census is practical. The population consists of the small number of players in a country, and it easy to obtain their heights.
A
In a Gallup poll of 1 comma 073 randomly selected American sportsmen, 89% said that cloning of humans should not be allowed. Identify the sample, population, and sampling method. Then comment on whether you think it is likely that the sample is representative of the population. Identify the sample. Choose the correct answer below. A: the 1 comma 073 randomly selected American sportsmen B: all American sportsmen C: sportsmen of the whole world D: 89% of randomly selected American sportsmen
A
In a Gallup poll of 1 comma 073 randomly selected American sportsmen, 89% said that cloning of humans should not be allowed. Identify the sample, population, and sampling method. Then comment on whether you think it is likely that the sample is representative of the population. Identify the sample. Choose the correct answer below. Comment on whether you think it is likely that the sample is representative of the population. Choose the correct answer below. A: The sample is fairly large and random. Assuming it was obtained by a reputable firm, the sample is likely to be representative of the population. B:The size of the sample is not equal to the size of the population, so the sample is likely to be representative of the population. C: The members of the sample have different characteristics than members of the population, so the sample is not likely to be representative of the population.
A
In a survey of 1,733 executives, it was found that 51% of them said that if they could start their careers again, they would choose a different field. The margin of error was 3 percentage points.Briefly describe the raw data for the study. Choose the correct answer below. A: Individual responses to the question B: The percentage of the 1,733 executives selected for the survey who said that if they could start their careers again, they would choose a different field C: The percentage of all executives who say that if they could start their careers again, they would choose a different field D: The 95% confidence interval
A
In a survey of 1,733 executives, it was found that 51% of them said that if they could start their careers again, they would choose a different field. The margin of error was 3 percentage points.Briefly describe the sample statistic for the study. Choose the correct answer below. A: 51% B: 3 percentage points C: 49% D: The 1,733 executives selected for the survey
A
The following claim might be addressed in an experiment: A company is developing a new plastic for remote control boats, and it is claimed that the new plastic lasts significantly longer than those currently in use. Would he design the experiment to be single-blind, double-blind, or neither? Select the correct answer below. A: Neither, because the remote control boats can't be affected by knowing which group it is in and the experimenter knowing won't affect the plastic longevity B: Double-blind, because it is always better to have more blinding C: Single-blind, because it can't be double-blind as the remote control boats will know what type of plastic is used D: Neither, because the researcher must know the group assignments and the remote control boats will know what type of plastic is used E: Single-blind, because the experimenter must know what plastic to use F: Double-blind, because the researcher or the subject knowing about the experiment will affect the results
A
A researcher plans to investigate the belief that people are more comfortable in the summer sun when they wear clothing with light colors instead of clothing with dark colors. Does it make sense to use a double-blind experiment in this case? Is it easy to implement blinding in this case? Explain. Does it make sense to use a double-blind experiment in this case? A: No, because the color of clothing a subject is wearing may have a psychological effect on how comfortable they feel in the sun. It could also influence how the researcher interacts with the subject. B: Yes, because the color of clothing a subject is wearing may have a psychological effect on how comfortable they feel in the sun. It could also influence how the researcher interacts with the subject. C: Yes, because the color of clothing a subject is wearing will not have any psychological effect on how comfortable they feel in the sun. D: No, because the color of clothing a subject is wearing will not have any psychological effect on how comfortable they feel in the sun.
B
In a Gallup poll of 1 comma 073 randomly selected American sportsmen, 89% said that cloning of humans should not be allowed. Identify the sample, population, and sampling method. Then comment on whether you think it is likely that the sample is representative of the population. Identify the sample. Choose the correct answer below. Identify the population. Choose the correct answer below. A: 89% of randomly selected American sportsmen B: all American sportsmen C: sportsmen of the whole world D: the 1 comma 073 randomly selected American sportsmen
B
In a survey of 1,733 executives, it was found that 51% of them said that if they could start their careers again, they would choose a different field. The margin of error was 3 percentage points. a. Based on the given information, state what you think was the goal of the study. Identify a possible population and the population parameter of interest. What is the goal of this study? Choose the correct answer below. A. To determine if executives can start their careers again B. To determine how satisfied executives are with their career choices C. To determine if executives have already changed the field of their work D. To determine when executives are going to start their careers again
B
In testing the effectiveness of a new vaccine, suppose that researchers used males for the treatment group and females for the placebo group. What is confounding, and how would it affect such an experiment? What is confounding? A: Confounding is when the researchers and subjects in a study do not know who is in the treatment group and who is in the control group. B: Confounding is the mixing of effects from different factors so that the effects from the specific factors being studied cannot be determined. C: Confounding is the process of making a sample more representative of the population. D: Confounding is the process of eliminating all differences between the groups in a study so that the only difference that remains is the factor of interest to the researcher.
B
The following claim might be addressed in an experiment: A company is developing a new plastic for remote control boats, and it is claimed that the new plastic lasts significantly longer than those currently in use. What would he choose as the control group? Select the correct answer below. A: Anything that uses a current plastic, because they did not receive the treatment B: Remote control boats that use a current plastic, because they did not receive the treatment C: Remote control boats, because they did not receive the treatment D: Anything that uses the new plastic, because they received the treatment E: Remote control boats that use the new plastic, because they received the treatment F: A current plastic, because it is the treatment
B
A pollster conducts a research project about how adult Chinese pay their bills. She posts her survey online and obtains 45 responses. Identify the population. A: Everyone who visited the website B: The 45 internet users who completed the survey C: All Chinese adults D: Adults of the whole world
C
Briefly describe the sample statistic for the study. Choose the correct answer below. A: The number of all adults who are unemployed B: 0.3 percentage points C: 4.6% D: 60,000 households selected for the survey
C
Define variables of interest. Select the correct answer below. A: The value that is applied to the treatment group B: Any single data point C: The items or quantities that the study seeks to measure in a statistical study D: Any item or quantity that has an unknown value
C
Determine whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). An educational researcher conducted a census to determine the average (mean) number of years it takes undergraduate statistics students to earn a college degree. Choose the correct answer and explanation from the choices below. A: The statement does not make sense because it does not account for students who changed majors to statistics or who double majored. B: The statement makes sense because a census would guarantee accuracy of the computed average. C: The statement does not make sense because it is not possible or practical to survey every undergraduate statistics student, as would be required for a census. D: The statement makes sense because a census is representative of the population and would suffice for the purposes of constructing an accurate average of how long it took the population of undergraduate statistics majors to earn a college degree.
C
In phase II testing of a new drug designed to increase the red blood cell count, a researcher obtains envelopes with the names and addresses of all treated subjects. She wants to increase the dosage in a sub-sample of 23 subjects, so she thoroughly mixes all of the envelopes in a bin, then pulls 23 of those envelopes to identify the subjects to be given the increased dosage. Is the procedure likely to yield a representative sample or a biased sample? Explain why. A: The procedure is likely to yield a biased sample because the researcher knows the patients from treating them previously and that will influence her decision as to which patient will get an increased dosage. B: The procedure is likely to yield a representative sample because the subjects are all chosen to be similar as part of the design of the experiment. Therefore, any sampling method will yield patients which are identical in all the aspects relevant to the study. C: The procedure is likely to yield a representative sample because there is no bias in the selection process. D: The procedure is likely to yield a biased sample because the subgroup size of 23 is too small.
C
The term statistics can have two meanings. Describe both meanings. Choose the correct answer below. A: Statistics is the science of collecting, organizing, and interpreting data and statistics is always definitive. B: Statistics is a type of algebra and statistics are variables in equations. C: Statistics is the science of collecting, organizing, and interpreting data and statistics are the data (numbers or other pieces of information) that describe or summarize something. D: Statistics is information used to make graphs and statistics are always numbers.
C
What is the third step in a statistical study?
Collect raw data from the sample and summarize these data by finding sample statistics of interest.
A college dean obtains an alphabetical list of all full-time students at her college and she selects every 35th name on that list and surveys those students to find the amount of student debt incurred by each of them. She uses the results to estimate the average (mean) amount of student debt incurred by college students in the United States.Is the procedure likely to yield a representative sample or a biased sample? Explain why. A: The procedure is likely to be representative because the study includes a large fraction of the student population of that university. B: The procedure is likely to yield a biased sample because students with similar last names tend to have similar amounts of student debt, and the numbers of students with similar last names is most likely not evenly distributed. C: The procedure is likely to yield a representative sample because there is no reason to suspect that every 35th student would have significantly more student debt compared with other students. D: The procedure is likely to yield a biased sample because the students she surveys are all from the same school.
D
A pollster conducts a research project about how adult Chinese pay their bills. She posts her survey online and obtains 45 responses. Identify the sample. A: Adults of the whole world B: All Chinese adults C: Everyone who visited the website D: The 45 internet users who completed the survey
D
A pollster conducts a research project about how adult Chinese pay their bills. She posts her survey online and obtains 45 responses. Identify the sampling method. A: Systematic sampling B: Stratified sampling C: Simple random sampling D: Convenience sampling E: Cluster sampling
D
Decide whether the statement below makes sense or does not make sense. Explain. There is no doubt that Johnson won the election, because an exit poll showed that she received 54% of the vote and the margin of error is only 3 percentage points. (Assume that all the people in the poll answered truthfully.) Choose the correct answer below. A: The statement does not make sense, because there is the possibility that Johnson lost the election, and the result is still within the margin of error. B: The statement makes sense, because all of the values contained in the confidence interval, determined by the sample statistic and the margin of error, give Johnson a majority (over 50% of the vote). C: The statement makes sense, because 54% is greater than 50%. D: The statement does not make sense, because there is always a possibility that a population parameter is not contained in the confidence interval determined by a sample statistic and a margin of error.
D
In testing the effectiveness of a new vaccine, suppose that researchers used males for the treatment group and females for the placebo group. What is confounding, and how would it affect such an experiment? How would it affect such an experiment? A: Confounding would make the results of the experiment more representative of the population. B: If males are given the treatment and females are given placebos, a researcher would be certain that any differences between the two groups are attributable to the treatment. C: The researchers would be confounded as to whether the males or the females are receiving the treatment. D: If males are given the treatment and females are given placebos, a researcher would not know whether effects are due to the treatment or the sex of the participant.
D
What is a representative sample, and why is it important? Choose the correct answer below. A: A representative sample is a sample where the members of the sample differ in some specific way from the members of the general population. Each representative sample is important because it offers a different representation of the population. B: A representative sample is a sample that represents one feature of a population more strongly than another. It's useful for studying a specific trait of a population but can lead to misleading inferences about other traits of the population. C: A representative sample is a sample in which all of the relevant members of the population are sampled. This type of sample is important because it gives complete knowledge about all members of the population who have the relevant trait. D: A representative sample is a sample in which the relevant characteristics of the sample members are generally the same as the characteristics of the population. This type of sample is important because only a representative sample can be used to make trustworthy inferences about the population.
D
What is a placebo? A: A placebo refers to a specific member of a sample from which data are collected. B: A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment. C: A placebo refers to any problem in the design or conduct of a statistical study that tends to favor certain results. D: A placebo is physically similar to a treatment, but it lacks any active ingredients, so it should not by itself produce any effects.
D
Why is it important in an experiment to test the effectiveness of a drug? A: A placebo exaggerates any psychological differences between the control group and the treatment group. B: A placebo makes the sample less representative of the population but the data can still be used to make inferences about the population. C: A placebo makes the sample more representative of the population. D: A placebo is important so that results from subjects given a treatment can be compared with the results from subjects given a placebo.
D
What is the fifth (and final) step of a statistic study?
Draw conclusions
In phase II testing of a new drug designed to increase the red blood cell count, a researcher obtains envelopes with the names and addresses of all treated subjects. She wants to increase the dosage in a sub-sample of 23 subjects, so she thoroughly mixes all of the envelopes in a bin, then pulls 23 of those envelopes to identify the subjects to be given the increased dosage. What type of sampling is used? A: Cluster sample B: Stratified sample C: Systematic sample D: Convenience sample E: Simple random sample
E
researchers apply some treatment and observe its effects on the subjects
experiment
variable that may explain or cause the effect
explanatory variable
Equation for calculating the range of values likely to contain the population parameter:
from (sample statistic-margin of error) to (sample statistic+margin of error)
A type of sampling in which we use a system such as choosing every 50th member of a population.
systematic sampling
