Stats Chapter 1 Homework 1.1b Statistical Study Design
experimental study
a study in which the researchers attempt to control one or more aspects of the individuals in the sample
In a study to add a new feature to a software program, the programmer introduced two categories, men and women, in the survey she conducted. Is the study observational or experimental? If it is an experiment, what is the controlled factor?
The study is an observational study. The samples are chosen using an appropriate process; however, no attempt is made to control any aspect of the sample even though the variables of interest are recorded for each group.
observational study
a study in which no attempt is made to control any aspect of the individuals in the sample
To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used?
Cluster sampling This scenario demonstrates cluster sampling. Cluster sampling involves dividing the population into groups and randomly selecting several of these groups.
Which of the following scenarios demonstrates sampling bias?
Kathryn wants to estimate the mean amount of money spent on clothes per week by mall shoppers. She collects data from every 10th person entering a clothing store at the mall. A sample is biased if some individuals of the population are more or less likely to be selected than others. The sample from choice B is biased because mall shoppers that do not visit this particular store are not represented.
Tina collected data from a random sample of 600 students in her university asking whether or not they exercise more than 30 minutes per day. Based on the results, she reports that 53% of the students in the nation exercise more than 30 minutes per day. Why is this statistic misleading?
The sample is biased. The sample in this case is biased. The individuals included in the sample are not representative of the entire population because the students at her school do not necessarily have the same exercise habits as the entire national student population.
A candy manufacturer is interested in the distribution of colors in each of its packages of candy sold. What should the researchers do first?
Write a question about the distribution of colors in each package. The researchers are at the starting point of the process. They first need to create a question or claim that is testable.
A study was conducted to determine whether a new highway should be built next to the river in a town. Half of the residents in the town live near the river. The sample of this study consisted of all the residents in the town who live near the river. Which of the following describes the sampling of this study?
There is sampling bias. Sampling bias exists in this study because the people who live near the river probably have stronger opinions about a new highway being placed next to their homes than the rest of the residents in the town who do not live close to the river.
Which of the following scenarios contains a sampling error?
A study is conducted to determine the favorite subject of all the students in your high school. Students in your homeroom class were used as the sample.
In reference to different sampling methods, is the following statement true or false? Systematic sampling includes the steps: identify individuals of the population that are easily accessible; obtain data from these individuals.
False Systematic sampling includes the steps: list the members of the population; use simple random sampling to select a starting point in the population; let k = (number of individuals in the population)/(number of individuals needed in the sample); choose every kth individual in the list starting with the one that was randomly selected. Convenience sampling includes the steps: identify individuals of the population that are easily accessible; obtain data from these individuals.
A study was performed with a random sample of 513 bolts produced at one factory. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?
The conclusions would apply to all bolts produced by that factory. Since the sample is fairly large and was randomly obtained, the results should apply to the bolts made at the factory in the study. However, there could be systematic differences between that factory and any other run by the same company, so the results should not be generalized any further.
After asking 11 randomly selected students from her school whether or not they read the newspaper , Gloria reports that 55% of the students from her school read the newspaper based on her survey. Why is this statistic misleading?
The sample size is insufficient. Although the sampling was random, using such a small sample size to draw conclusions about a much larger number of individuals is bound to be unreliable. This sample size is too small.
A biology student is interested in the relationship between temperature and germination time for soy beans. The student gets sample seeds from multiple sources and randomly selects 180 seeds from them. Then he sets up three growing stations, one at 20∘C, one at 15∘C, and one at 25∘C. He divides the seeds into three groups of 60 and plants the seeds from each group in a growing station. He records the germination time for each seed. Is this an observational study or an experiment? If it is an experiment, what is the controlled factor?
The study is an experiment. The controlled factor is the temperature. Since the seeds are divided into three groups and each group is subjected to a controlled temperature, the study is an experiment. The temperature is the controlled factor.
Is a survey of the guests about their preference of food at a party an observational study or experimental study? If it is an experiment, what is the controlled factor?
The study is an observational study. The samples are chosen using an appropriate process; however, no attempt is made to control any aspect of the sample even though the variables of interest are recorded for each group.
Which of the following is the situation in which not all members of the population are equally likely to be selected?
sampling bias A sampling bias is defined as the situation in which not all members of the population are equally likely to be selected
A sampling bias is defined as _______.
the situation in which not all members of the population are equally likely to be selected A sampling bias is defined as the situation in which not all members of the population are equally likely to be selected.
A researcher is interested in the effects of watching videos just before bed on the quality of sleep. He has decided to test the claim "Watching 1 hour of video just before going to bed reduces the number of minutes of REM sleep by more than 10%. " Which of the following data collection processes would be appropriate? Select only one answer choice.
Choose a random sample of people. On multiple randomly selected nights, randomly assign each person to either watch one hour of video or not watch video and monitor their sleep. To perform an experiment, a control group that does not watch video and a test group that does should be used. It is also important for the process to account for possible confounding variables. In this case both the person and the night of the week could be confounding variables. By choosing random nights and having the same people either watch 1 hour of videos or not, variations due to the person and the night of the week should not interfere with the analysis
Which of the following scenarios contain nonbiased samples? Select all that apply.
Christine wants to estimate the mean grade point average of students at her school. She collects data by recording the grade point average of every 25th student on the list of students after a randomly selected first student. Homer wants to estimate the ethnic background distribution of residents of his town. He collects data from 1000 randomly selected town residents by using a random number generator. To estimate the mean salary of professors at his university, Peter collects data by recording the salaries of all professors included in 12 randomly selected departments. A sample is biased if some individuals of the population are more or less likely to be selected than others. The sample from choice A is nonbiased because every student has an equal chance of being selected. The sample from choice B is nonbiased because every resident has an equal chance of being selected. The sample from choice D is nonbiased because every professor has an equal chance of being selected.
Which of the following scenarios contain biased samples? Select all that apply.
Howard wants to estimate the mean weight of people in his town. He collects data by interviewing members of a fitness club. To estimate the political party distribution of residents in his state, Sean collects data from a large group of randomly selected residents of his city. Teresa wants to estimate the mean amount of money spent on clothes per week by mall shoppers. She collects data from every 10th person entering a clothing store at the mall. A sample is biased if some individuals of the population are more or less likely to be selected than others. The sample from choice B is biased because members of the fitness club will have different exercise and eating habits than the rest of the population. The sample from choice C is biased because this specific city is most likely not representative of the entire state depending on its demographics. The sample from choice D is biased because mall shoppers that do not visit this particular store are not represented.
Select all of the following scenarios below that contain biased samples.
Kelly wants to estimate the mean number of calories consumed by students at her school. She collects data from randomly selected individuals in the cafeteria for breakfast. To estimate the mean amount of money spent on clothes per week by mall shoppers, Paul collects data from every 10th person entering a clothing store at the mall. A sample is biased if some individuals of the population are more or less likely to be selected than others. The sample from choice A is biased because students that do not eat breakfast are not included in the sample. The sample from choice C is biased because mall shoppers that do not visit this particular store are not represented.
A candy manufacturer is interested in the distribution of colors in each of its packages of candy sold. The manufacturer randomly sample packages from multiple batches at one factory. Are the results generalizable to the company's other factories that produce the same candy?
No, because the other factories may have different processes or the settings on the machines may be different. Since no data was obtained from any other factories, the sample is only applicable to the factory involved in the study. There are many unknown variables that could affect the color distribution, so the results cannot be generalized to other places.
A statistics student is doing a project for her class. She wants to make a prediction for the outcome of an upcoming national election. Since there are only two candidates, she decides that her question is "Which candidate do more people favor in the upcoming election?" She decides to randomly interview 100 students crossing the courtyard on campus about their preference. Is this sample good for drawing general conclusions about the results of the election?
No. The results are not generalizable because the students at her school are not representative of the population of all voters. Since the students at a college are not representative of the population of a country as a whole, even a well-chosen random sample of the students is not generalizable to the whole population. The results should not be considered useful for predicting the outcome of the election.
Which of the following scenarios contain biased samples? Select all that apply.
Ruth wants to estimate the mean height of students at her school. She collects data by selecting a random group of students within her classroom. Jennifer wants to estimate the mean amount of money spent on clothes per week by mall shoppers. She collects data from every 10th person entering one clothing store at the mall. To estimate the political party distribution of residents in his state, Patrick collects data from a large group of randomly selected residents of his city. A sample is biased if some individuals of the population are more or less likely to be selected than others. The sample from choice A is biased because the students in this classroom may only represent one grade level, which could be shorter or taller in general than other grade levels. The sample from choice B is biased because mall shoppers that do not visit this particular store are not represented. The sample from choice D is biased because this specific city is most likely not representative of the entire state depending on its demographics.
A consumer research company is interested in determining if a certain company's new refrigerator model is more efficient than the older model. Researchers decide to investigate the claim that the new model uses 10% less electricity than the older model for the same cooling load. To collect data, the company obtains 20 random refrigerators for each model. They are all placed in one building well separated from each other and are loaded with 50 bottles of water. The electricity usage is monitored for one month. How can the results be generalized?
The conclusions should be applicable to any unit of the new model as compared to any unit of the old model. Since the samples were randomly obtained for both the new and old models in question, the results should apply to both the new and old model refrigerator that was studied. The conclusions should then generalize to any unit of the new and old models.
A cell phone company advertises that their average plan rate is $73. Given that their plan rates are $9, $82, $95, and $106, why is this statistic misleading?
The data contains an outlier. The average of these plan rates is accurate, but the advertised average is misleading because so many of the plan rates are well above this level. The very low plan rate is an outlier and brings the average down to a misleading value.
A candy manufacturer is interested in the distribution of colors in each of its packages of candy sold. The manufacturer wants to answer the question "What is the typical distribution of colors in a package of candy?" Which data collection method should be used?
The manufacturer should randomly sample packages at the factory over multiple batches and determine the distribution in each package. To determine a typical distribution, multiple packages are needed. The packages should be representative of all packages produced at the factory, so randomly chosen packages from multiple batches would be best.
A researcher is interested in the effects of watching videos just before bed on the quality of sleep. He has decided to test the claim "Watching 1 hour of video just before going to bed reduces the number of minutes of REM sleep by more than 10%." How should the number of hours of video be treated?
The number of hours of video should be controlled. Some measurements should be done for 1 hour of video and some should be done with no video. The number of hours of video is an experimental factor that needs to be controlled. The claim specifies 1 hour. So there should be a test set for people who watched 1 hour of video and a control set for people who watched no video.
An opinion poll was conducted to know whether parents play a role in shaping a career for their children. Respondents were asked to vote "Yes" if they think parents have a role to play and "No" if they think parents have no role to play in shaping the career of their children. Is the study observational or experimental? If it is an experiment, what is the controlled factor?
The study is an observational study. The samples are chosen using an appropriate process; however, no attempt is made to control any aspect of the sample even though the variables of interest are recorded for each group.
Is the statement below true or false? A sampling bias is the situation in which not all members of the population are equally likely to be selected.
True A sampling bias is defined as the situation in which not all members of the population are equally likely to be selected.
Which of the following is most likely an example of a non-sampling error?
Two researchers distribute paper questionnaires to find out which of several candidates for city council is preferred before the election. The first researcher realizes later that several of the questionnaires he distributed were misprinted and left off one of the candidates. Two researchers create an online poll to find out whether people primarily use a computer, a smartphone, or a tablet to surf the web. After collecting their data, they realize that a bug made it harder for people with a smartphone to submit a response to the survey. In the case of the city council questionnaires, the printing error likely caused the data to be inaccurate. This is a non-sampling error because this error was not a result of the sampling that was done. Similarly, the bug in the online poll would cause inaccuracies in the data. But because the error was not a result of the sample and how it was chosen, it is also a non-sampling error.
Which of the following is most likely an example of a non-sampling error? Select all correct answers.
Two researchers distribute paper questionnaires to find out which of several candidates for city council is preferred before the election. The first researcher realizes later that several of the questionnaires he distributed were misprinted and left off one of the candidates. Two researchers create an online poll to find out whether people primarily use a computer, a smartphone, or a tablet to surf the web. After collecting their data, they realize that a bug made it harder for people with a smartphone to submit a response to the survey. In the case of the city council questionnaires, the printing error likely caused the data to be inaccurate. This is a non-sampling error because this error was not a result of the sampling that was done. Similarly, the bug in the online poll would cause inaccuracies in the data. But because the error was not a result of the sample and how it was chosen, it is also a non-sampling error.
