Test 1 Practice Questions
An experiment is being designed to compare relief from hay fever symptoms given by a low dose of a drug, a high dose of the drug, and a placebo. Each subject who suffers from hay fever and volunteers for the study is observed on three separate days, with a different treatment used each day. There are two days between treatments, so a treatment does not have a carry-over effect for the next treatment assigned. (b) Suppose the study is conducted as a double-blind study. Explain what this means.
Both the researchers and the subjects are not aware which treatment is being administered.
Choose whether an experiment or an observational study would be more appropriate to investigate the following. (c) Whether or not endorsement from a medalist makes someone more likely to purchase a box of cereal.
Experiment because stores can be assigned to receive either boxes with the endorsement packaging or without the endorsement packaging.
Consider the population of all students at your university. A certain proportion support mandatory national service (MNS) following high school. Your friend randomly samples 20 students from the school, and uses the sample proportion who support MNS to predict the population proportion at the school. You take your own, separate random sample of 20 students from this school and find the sample proportion that supports MNS. (b) For the two studies, are the sample proportions necessarily the same? Explain.
No. Different samples from the same population may result in different sample proportions.
In a study by Swedish researchers, 2410 women who had worked as hairdressers and given birth to children were compared to 3462 women from the general population who had given birth. The hairdressers had a slightly higher percentage of infants with a birth defect. (d) Can we conclude that there's something connected with being a hairdresser that causes higher rates of birth defects? Explain.
No. We can say there appears to be an association between the two variables, but we cannot say one causes the other. There is the possibility that a lurking variable is affecting the result
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2020, but statisticians might be more interested in the processes behind exit polling and the reliability of their results. When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents. Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed. (c) What problems might arise from Democrats being more likely to participate in exit polls than the other groups?
Nonresponse Bias
A newspaper in Los Angeles designs a survey to estimate the proportion of the city's adult residents who favor a proposal to legalize casinos in the city. It takes a list of the 1000 people who have subscribed to the paper the longest, and sends each of them a questionnaire that asks, "Do you think it is a good idea to legalize casinos in Los Angeles, which will broaden the tax base and contribute money to education?" After analyzing results from the 50 people who reply, they report that 90% of the Los Angeles citizens are in favor of the proposal. Identify the following sources of bias. (a) Bias due to undercoverage.
Not all parts of the Los Angeles population have representation.
Choose whether an experiment or an observational study would be more appropriate to investigate the following. (a) Whether or not smoking has an effect on coronary heart disease.
Observational study because smoking is not a treatment that can be ethically imposed on subjects.
Choose whether an experiment or an observational study would be more appropriate to investigate the following. (b) Whether or not higher SAT scores tend to be positively associated with higher college GPAs.
Observational study because subjects cannot be told to have a higher SAT score.
In a study by Swedish researchers, 2410 women who had worked as hairdressers and given birth to children were compared to 3462 women from the general population who had given birth. The hairdressers had a slightly higher percentage of infants with a birth defect. (c) Is this an observational study or an experiment? Explain.
Observational study because women chose to be hairdressers and were not told to do so as part of the study.
An experiment is being designed to compare relief from hay fever symptoms given by a low dose of a drug, a high dose of the drug, and a placebo. Each subject who suffers from hay fever and volunteers for the study is observed on three separate days, with a different treatment used each day. There are two days between treatments, so a treatment does not have a carry-over effect for the next treatment assigned. (c) Explain how randomization could easily be incorporated into this study while maintaining that each subject participates in all three treatments.
Randomize the order of the treatments being administered for each subject.
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2020, but statisticians might be more interested in the processes behind exit polling and the reliability of their results. When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents. Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed. (b) Why do the polling companies randomly select the precincts to visit?
Randomly selecting precincts increases the likelihood that the people polled represent the population well.
(d) If the experiment is properly randomized and the study reveals a statistical difference between treatments, which of the following is true? i. The study can conclude that the treatment is the cause of the difference in hay fever symptoms. ii. The results of the study can be generalized to the population of all hay fever sufferers
Statement i is correct.
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2020, but statisticians might be more interested in the processes behind exit polling and the reliability of their results. When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents. Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed. (a) What type of sampling methods are used in selecting people for exit polls at the polling locations? Select all that apply.
Systematic Sampling and Cluster Sampling
A newspaper in Los Angeles designs a survey to estimate the proportion of the city's adult residents who favor a proposal to legalize casinos in the city. It takes a list of the 1000 people who have subscribed to the paper the longest, and sends each of them a questionnaire that asks, "Do you think it is a good idea to legalize casinos in Los Angeles, which will broaden the tax base and contribute money to education?" After analyzing results from the 50 people who reply, they report that 90% of the Los Angeles citizens are in favor of the proposal. Identify the following sources of bias. (c) Nonresponse bias.
The few who take the time to respond might not be representative of the population.
A newspaper in Los Angeles designs a survey to estimate the proportion of the city's adult residents who favor a proposal to legalize casinos in the city. It takes a list of the 1000 people who have subscribed to the paper the longest, and sends each of them a questionnaire that asks, "Do you think it is a good idea to legalize casinos in Los Angeles, which will broaden the tax base and contribute money to education?" After analyzing results from the 50 people who reply, they report that 90% of the Los Angeles citizens are in favor of the proposal. Identify the following sources of bias. (d) Response bias due to the way the question was asked.
The question frames the proposal in a positive way, which may skew the responses.
A popular news website posted a survey asking, "Do you read the end-user license agreements when installing software or games?" Of the 26,841 respondents, 64% said they never read these agreements. (b) How much confidence would you place in using 64% as an estimate of the fraction of people who don't read software licenses?
There should be no confidence because the true parameter cannot be estimated from a self-selected sample.
A newspaper in Los Angeles designs a survey to estimate the proportion of the city's adult residents who favor a proposal to legalize casinos in the city. It takes a list of the 1000 people who have subscribed to the paper the longest, and sends each of them a questionnaire that asks, "Do you think it is a good idea to legalize casinos in Los Angeles, which will broaden the tax base and contribute money to education?" After analyzing results from the 50 people who reply, they report that 90% of the Los Angeles citizens are in favor of the proposal. Identify the following sources of bias. (b) Bias due to the sampling design.
They do not use random sampling.
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2020, but statisticians might be more interested in the processes behind exit polling and the reliability of their results. When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents. Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed. (d) Why do the polling companies try to contact people who voted early?
To prevent undercoverage in their polling.
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2020, but statisticians might be more interested in the processes behind exit polling and the reliability of their results. When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents. Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed. (e) If people who vote in the last few hours of the day are different from those who vote at other times, what problems would this cause?
Undercoverage Bias
The Environmental Protection Agency (EPA) uses a few new automobiles of each model every year to collect data on pollution emission, gasoline mileage performance, number of cylinders, and weight. For the Honda Accord model, identify what's meant by the following. (d) Population
all new Honda Accords
Commercials for an energy bracelet claim that it helps with balance and coordination. To test this claim, a random sample of 100 people are selected at a nearby mall and asked to balance on one leg as long as they can. Then these same people are asked to put on the energy bracelet and asked again to balance on one leg for as long as they can. (a) The measured variable, energy bracelet presence, is
categorical
A sample of 40 students will be selected from a list of 19200 registered students. Select the name of each sampling method described. (e) Assume all students live in dorms, with 10 single rooms per floor. Randomly select 4 floors from all dorms, and include all of the students living on the floors selected.
cluster sampling
A sample of 40 students will be selected from a list of 19200 registered students. Select the name of each sampling method described. (d) Select the first 40 students you pass by on campus.
convenience sampling
An experiment is being designed to compare relief from hay fever symptoms given by a low dose of a drug, a high dose of the drug, and a placebo. Each subject who suffers from hay fever and volunteers for the study is observed on three separate days, with a different treatment used each day. There are two days between treatments, so a treatment does not have a carry-over effect for the next treatment assigned. (a) What are the treatments in this study?
low dose, high dose, and placebo
Commercials for an energy bracelet claim that it helps with balance and coordination. To test this claim, a random sample of 100 people are selected at a nearby mall and asked to balance on one leg as long as they can. Then these same people are asked to put on the energy bracelet and asked again to balance on one leg for as long as they can. (b) Identify the type of design used in this experiment.
matched pairs design
For the entire city of Athens, the average income is $33,060, and 37.8% of the residents are below the poverty line. A local researcher does not have this information, so she tries to estimate these values by taking a random sample of 200 citizens of Athens. In her sample, the average income is $38,150, and 25% of the citizens in her sample were below the poverty line. (d) Which symbol below would denote the value of 0.378 in this example?
p
For the entire city of Athens, the average income is $33,060, and 37.8% of the residents are below the poverty line. A local researcher does not have this information, so she tries to estimate these values by taking a random sample of 200 citizens of Athens. In her sample, the average income is $38,150, and 25% of the citizens in her sample were below the poverty line. (e) $33,060 and 0.378 are examples of:
parameters
For the entire city of Athens, the average income is $33,060, and 37.8% of the residents are below the poverty line. A local researcher does not have this information, so she tries to estimate these values by taking a random sample of 200 citizens of Athens. In her sample, the average income is $38,150, and 25% of the citizens in her sample were below the poverty line. (a) The entire city of Athens is the:
population
For the entire city of Athens, the average income is $33,060, and 37.8% of the residents are below the poverty line. A local researcher does not have this information, so she tries to estimate these values by taking a random sample of 200 citizens of Athens. In her sample, the average income is $38,150, and 25% of the citizens in her sample were below the poverty line. (b) The 200 citizens from the researcher's data is the:
sample
A sample of 40 students will be selected from a list of 19200 registered students. Select the name of each sampling method described. (c) Put all of the student names on tickets and put the tickets in a container. Randomly select 40 tickets from the container.
simple random sampling
A sample of 40 students will be selected from a list of 19200 registered students. Select the name of each sampling method described. (a) Sort the students by class. Then use random numbers to select 10 Freshmen, 10 Sophomores, 10 Juniors, and 10 Seniors.
stratified sampling
A sample of 40 students will be selected from a list of 19200 registered students. Select the name of each sampling method described. (b) Randomly select a student between 1 and 480. Then select every 480 th student after that.
systematic sampling
The Environmental Protection Agency (EPA) uses a few new automobiles of each model every year to collect data on pollution emission, gasoline mileage performance, number of cylinders, and weight. For the Honda Accord model, identify what's meant by the following. (a) Subject
the new Honda Accord car
The Environmental Protection Agency (EPA) uses a few new automobiles of each model every year to collect data on pollution emission, gasoline mileage performance, number of cylinders, and weight. For the Honda Accord model, identify what's meant by the following. (c) Sample
the new Honda Accord that are chosen for the study
(i) True or False:Due to chance or natural variability, the sample means can be different even if there is no true difference in the population means.
true
(ii) True or False: The difference between two sample means may not be *statistically significant* because the difference may be small enough to be accounted for by chance or natural variability.
true
A popular news website posted a survey asking, "Do you read the end-user license agreements when installing software or games?" Of the 26,841 respondents, 64% said they never read these agreements. (a) What type of sample was this?
voluntary response sample
The Environmental Protection Agency (EPA) uses a few new automobiles of each model every year to collect data on pollution emission, gasoline mileage performance, number of cylinders, and weight. For the Honda Accord model, identify what's meant by the following. (b) Variable
weight, pollution emission, number of cylinders, and gasoline mileage
In a study by Swedish researchers, 2410 women who had worked as hairdressers and given birth to children were compared to 3462 women from the general population who had given birth. The hairdressers had a slightly higher percentage of infants with a birth defect. (a) Identify the explanatory variable:
whether woman was a hairdresser
In a study by Swedish researchers, 2410 women who had worked as hairdressers and given birth to children were compared to 3462 women from the general population who had given birth. The hairdressers had a slightly higher percentage of infants with a birth defect. (b) Identify the response variable.
whether woman's infant had a birth defect
For the entire city of Athens, the average income is $33,060, and 37.8% of the residents are below the poverty line. A local researcher does not have this information, so she tries to estimate these values by taking a random sample of 200 citizens of Athens. In her sample, the average income is $38,150, and 25% of the citizens in her sample were below the poverty line. (c) Which symbol below would denote the value of $38,150 in this example?
x bar
Consider the population of all students at your university. A certain proportion support mandatory national service (MNS) following high school. Your friend randomly samples 20 students from the school, and uses the sample proportion who support MNS to predict the population proportion at the school. You take your own, separate random sample of 20 students from this school and find the sample proportion that supports MNS. (a) For the two studies, are the populations the same?
yes