Statistics Chapter 1
The variable "eye color" is an example of what type of variable?
Categorical
The outcome variable in a question about causality is also referred to as what?
The response variable
A hospital employs 353 nurses and 34% of them are male. How many male nurses are there?
There are 120 male nurses.
A large law firm is made up of 60% male lawyers, or 165 male lawyers. What is the total number of lawyers at the firm?
There are 275 lawyers at the firm.
An engineering firm employs 170 engineers and 108 of them are male. What percentage of these engineers are female?
36.5% of the engineers are female.
In statistics, the data we work with is just one part of a bigger picture called the ____.
In statistics, the data we work with is just one part of a bigger picture called the population.
The number of times a value is observed in a data set is called a ______.
The number of times a value is observed in a data set is called a frequency.
The process of representing categorical variables with numbers (such as letting a 1 represent "smoker" and a 0 represent "non-smoker") is called _______.
The process of representing categorical variables with numbers (such as letting a 1 represent "smoker" and a 0 represent "non-smoker") is called coding.
The study of statistics rests on what two major concepts?
Variation and data
Of the following, which is the only method of data collection suitable for making conclusions about causal relationships?
Controlled experiments
Data are more than just numbers, because data have _____.
Data are more than just numbers, because data have context.
A doctor who believes strongly that antidepressants work better than "talk therapy" tests depressed patients by treating half of them with antidepressants and the other half with talk therapy. After six months the patients are evaluated on a scale of 1 to 5, with 5 indicating the greatest improvement. A. The doctor is concerned that if his most severely depressed patients do not receive the antidepressants, they will get much worse. He therefore decides that the most severe patients will be assigned to receive the antidepressants. Explain why this will affect his ability to determine which approach works best.
If the doctor decides on the treatment, this could introduce bias.
A doctor who believes strongly that antidepressants work better than "talk therapy" tests depressed patients by treating half of them with antidepressants and the other half with talk therapy. After six months the patients are evaluated on a scale of 1 to 5, with 5 indicating the greatest improvement. C. The doctor asks you whether it is acceptable for him to know which treatment each patient receives and to evaluate them himself at the end of the study to rate their improvement. Explain why this practice will affect his ability to determine which approach works best.
If the doctor is aware of the treatment each patient receives, that might influence his opinion about the effectiveness of the treatment.
A group of overweight people are asked to participate in a weight loss program. Participants are allowed to choose whether they want to go on a vegetarian diet or follow a traditional low-calorie diet that includes some meat. Half of the people choose the vegetarian diet, and half choose to be in the control group and continue to eat meat. Suppose that there is greater weight loss in the vegetarian group. A. Suggest a plausible confounding variable that would prevent us from concluding that the weight loss was due to the lack of meat in the diet. Explain why it is a confounding variable.
People who are not prepared to change their diet very much (such as by excluding meat) might also not change other factors that affect weight, such as how much exercise they get.
Which of the following is a reason we can never draw cause-and-effect conclusions from observational studies?
Potential confounding variables may explain the differences between groups rather than the treatment variable.
Questions about causality are usually phrased in the form of ___ questions.
Questions about causality are usually phrased in the form of "What if...?" questions.
Indicate whether the study is an observational study or a controlled experiment. A student watched picnickers with a large cooler of soft drinks to see whether teenagers were less likely than adults to choose diet soft drinks over regular soft drinks.
The study is an observational study.
It was predicted that a country will have an elderly population (65 and older) of 7,147,000 in the year 2050 and that this will be 18.4% of the population. What is the total predicted population of this country in 2050?
The total predicted population of the country in 2050 is 38842000 people. (Round to the nearest thousand people as needed.)
A doctor reported on a study that treated children who had sleep apnea, which interferes with breathing while a child is asleep. In the study, 464 children, 5 to 9 years of age, were randomly assigned to either surgery or to be under constant watch for a certain period of time. The study found that there were significantly greater improvements in behavioral, quality-of-life, and sleep study findings in the group that had surgery than the group assigned to constant watch B. Assuming that the study was properly conducted, can we conclude that the early surgery caused the improvements? Explain.
We can conclude that the early surgery caused the improvements because it was a randomized controlled experiment.
A different class has 268 students, and 57.5% of them are men. How many men are in the class?
b. There are 154 males in the class.
A difference between two groups in an observational study that can explain why the outcomes were very different between the groups is called what?
A confounding variable
Which of the following is an identifying mark of an observational study?
Subjects in the study are put into the treatment group or the control group either by their own actions or by the decision of someone not involved in the research study.
The circles shown to the right are similar, but not exactly the same. This is an example of _______.
The circles shown to the right are similar, but not exactly the same. This is an example of variation.
A doctor who believes strongly that antidepressants work better than "talk therapy" tests depressed patients by treating half of them with antidepressants and the other half with talk therapy. After six months the patients are evaluated on a scale of 1 to 5, with 5 indicating the greatest improvement. B. What advice would you give the doctor to improve his study?
The doctor should randomly assign the patients to the different treatments
Which of the following is used to summarize two potentially related categorical variables?
A two-way table
Categorical variables are also referred to as ______ variables.
Categorical variables are also referred to as qualitative variables.
A different class is made up of 66% women and has 17 women in it. What is the total number of students in the class?
The class consists of 26 students.
In an experiment studying the association between a treatment variable and an outcome variable, the group of people who do NOT receive the treatment are called what?
The control group
Two drugs were tested to see whether they helped women with breast cancer. Of 1060 women, about half were randomly assigned to drug A and the other half were assigned to drug B. After 77 months, 473 out of 539, and 426 out of 521 women assigned to drugs A and B, respectively, were alive. Was this a controlled experiment or an observational study? Explain why. From studies like these, can we conclude a cause-and-effect relationship between the drug type and the survival percentage? Why or why not?
This is a controlled experiment because the researchers randomly determined the groups. We can conclude a cause-and-effect relationship because the women were randomly assigned to the treatment and control groups, which controls for other variables.
Indicate whether the following study is an observational study or a controlled experiment. A researcher is interested in the effect of music on memory. She randomly divides a group of students into three groups: those who will listen to quiet music, those who will listen to loud music, and those who will not listen to music. After the appropriate music is played (or not played), she gives all the students a memory test.
This is a controlled experiment. She assigns students to the control and treatment groups at random in order to control for all relevant factors aside from the effect of music on memory, which is essential to conducting a controlled experiment.
Indicate whether the following study is an observational study or a controlled experiment. Records of patients who have had broken ankles are examined to see whether those who had physical therapy achieved more ankle mobility than those who did not.
This is an observational study. Since the researchers did not assign subjects to the control or treatment group beforehand, they did not satisfy a key feature of controlled experiments.
Indicate whether the following study is an observational study or a controlled experiment. A local public school encourages, but does not require, students to wear uniforms. The principal of the school compares the grade point averages of students at this school who wear uniforms with the GPAs of those who do not wear uniforms to determine whether those wearing uniforms tend to have higher GPAs.
This is an observational study. The principal does not randomly assign students to either wear or not wear uniforms. Random assignment is essential to conducting a controlled experiment.
What are two basic types of variables in statistics? Numerical and algebraic Numerical and categorical Contextual and categorical Numerical and contextual
Numerical and categorical
Which of the following is NOT one of the criteria for the "gold standard" for experiments?
Equal sample sizes for control and treatment group
A study looked at the effects of light on female mice. Fifty mice were randomly assigned to a regimen of 12 hours of light and 12 hours of dark (LD), while another fifty mice were assigned to 24 hours of light (LL). Researchers observed the mice for two years. Three of the LD mice and 15 of the LL mice developed tumors. Determine the percentage of mice that developed tumors from each group (LL and LD). Compare them and comment
In the LD mice, 6% developed tumors. In the LL mice, 30% developed tumors. The LD mice developed tumors at a lower rate than the LL mice.
In statistics, variables are _____.
In statistics, variables are characteristics of people or things.
A group of overweight people are asked to participate in a weight loss program. Participants are allowed to choose whether they want to go on a vegetarian diet or follow a traditional low-calorie diet that includes some meat. Half of the people choose the vegetarian diet, and half choose to be in the control group and continue to eat meat. Suppose that there is greater weight loss in the vegetarian group. B. Explain a better way to do the experiment that is likely to remove the influence of confounding variables.
The experiment would be improved if some subjects were randomly assigned to eat meat and the remaining subjects to consume a vegetarian diet.
A statistics class is made up of 18 men and 17 women. What percentage of the class is male?
The statistics class is 51.4% male.
Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m. The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do. What information is missing that might contradict this claim?
The percentage of female students in the two classes is unknown. There may be more females in the 8 a.m. because there are more students in the 8 a.m. class than the 10 a.m. class. This claim could be true only if the classes were the same size.
It was reported in 2007 that there were 8,286,000 people age 16 or older who had a "go outside the home" disability and that this was 21.8% of the population (of this age group). These are people who cannot go outside the home without help. How large was the total population (of this age group) in 2007?
The population in 2007 of people (of this age group) is 38009000 people. (Round to the nearest thousand people as needed.)
Indicate whether the study is an observational study or a controlled experiment. A researcher was interested in the effects of exercise on academic performance in elementary school children. She went to the recess area of an elementary school and identified some students who were exercising vigorously and some who were not. The researcher then compared the grades of the exercisers with the grades of those who did not exercise.
The study is an observational study.
Why are percentages or rates often better than counts for making comparisons?
They take into account possible differences among the sizes of the groups.
Which of the following questions should be asked when developing an understanding of data? A. Who collected the data? B. What variables were measured? C. How were the variables measured? D. All of these questions are important.
All of these questions are important.
A study looked at the effects of light on female mice. Fifty mice were randomly assigned to a regimen of 12 hours of light and 12 hours of dark (LD), while another fifty mice were assigned to 24 hours of light (LL). Researchers observed the mice for two years. Three of the LD mice and 15 of the LL mice developed tumors. Can we conclude that light for 24 hours a day causes an increase in tumors in mice? Why or why not?
Because it was a controlled experiment, it can be concluded that light for 24 hours a day causes an increase in tumors in mice.
A study was done to see whether a smaller dose of flu vaccine could be used successfully. In this study, the usual amount of vaccine was injected into half the patients, and the other half of the patients had only a small amount of vaccine injected. The response was measured by looking at the production of antibodies. In the end, the lower dose of vaccine was just as effective as a higher dose for those under 65 years old. What more do we need to know to be able to conclude that the lower dose of vaccine was equally effective at preventing the flu for those under 65? A. This is a controlled experiment and causation cannot be inferred. B. The sample size must be at least 500 to ensure the sample size is large enough to infer causation. C. This is an observational study and causation cannot be inferred. D. The patients need to be randomly assigned the full or lower dose. Without randomization there could be bias, however, with randomization we can infer causation.
D. The patients need to be randomly assigned the full or lower dose. Without randomization there could be bias, however, with randomization we can infer causation.
In 2008, a highway safety administration reported that the number of pedestrian fatalities in City A was 65 and that the number in City B was 45. Can we conclude that pedestrians are safer in City B? Why or why not?
No, in order to compare the fatalities the statistics must include the number of fatalities per pedestrian. There may be fewer pedestrians in City B causing the difference.
A doctor reported on a study that treated children who had sleep apnea, which interferes with breathing while a child is asleep. In the study, 464 children, 5 to 9 years of age, were randomly assigned to either surgery or to be under constant watch for a certain period of time. The study found that there were significantly greater improvements in behavioral, quality-of-life, and sleep study findings in the group that had surgery than the group assigned to constant watch A. Was the study a controlled experiment or an observational study? Explain how you know.
The study was a controlled experiment because the children were randomly assigned to either surgery or constant watch. This is essential to conducting a controlled experiment.
A study looked at the effects of light on female mice. Fifty mice were randomly assigned to a regimen of 12 hours of light and 12 hours of dark (LD), while another fifty mice were assigned to 24 hours of light (LL). Researchers observed the mice for two years. Three of the LD mice and 15 of the LL mice developed tumors. Was this a controlled experiment or an observational study? How do you know?
This was a controlled experiment because there were two groups that were assigned by the researchers.
Some people believe that wearing copper bracelets is a good treatment for arthritis of the hand. To test this belief, suppose you recruit 100 people and supply them all with copper bracelets. After the patients wear the bracelets for a month, you ask them whether or not their pain is less than it was before they began wearing the bracelets. Explain how to improve this study.
To improve the study, the patients should be randomly divided into two groups; one group will be given the copper bracelets, and the other group will be given non-copper bracelets. After a month, the patients will be surveyed on the levels of their pain.
Why is random assignment used to assign people to treatment groups and control groups in a controlled experiment?
To make the groups as similar as possible, minimizing bias.
Two drugs were tested to see whether they helped women with breast cancer. Of 1060 women, about half were randomly assigned to drug A and the other half were assigned to drug B. After 77 months, 473 out of 539, and 426 out of 521 women assigned to drugs A and B, respectively, were alive.
a. The survival rate for drug A is 87.8%. The survival drug for drug B is 81.8%. The survival rate for drug A is higher than the survival rate for drug B.
A group of educators want to determine how effective tutoring is in raising students' grades in a math class, so they arrange free tutoring for those who want it. Then they compare final exam grades for the group that took advantage of the tutoring and the group that did not. Suppose the group participating in the tutoring tended to receive higher grades on the exam. Does that show that the tutoring worked? If not, explain why not and suggest a confounding variable.
Because this was an observational study, it only shows an association; it does not show that the tutoring worked. It could be that more motivated students attended the tutoring and that was what caused the higher grades.
A study concludes that the use of pesticides is associated with the development of Parkinson's disease, a neurological disease that causes people to shake. The study reported that exposure to bug killers and weed killers is "associated with" an increase of 33% to 80% in the chances of getting Parkinson's. Does this study show that pesticides cause Parkinson's disease? Why or why not?
The study does not show that pesticides cause Parkinson's disease. This was an observational study because researchers could not have deliberately exposed people to pesticides. Observational studies cannot conclude causation.
Indicate whether the study is an observational study or a controlled experiment. A group of boys is randomly divided into two groups. One group watches violent cartoons for one hour, and the other group watches cartoons without violence for one hour. The boys are then observed to see how many violent actions they take in the next two hours, and the two groups are compared.
The study is a controlled experiment.
A doctor who believes strongly that antidepressants work better than "talk therapy" tests depressed patients by treating half of them with antidepressants and the other half with talk therapy. After six months the patients are evaluated on a scale of 1 to 5, with 5 indicating the greatest improvement. D. What improvements to the plan in part (c) would you recommend?
To prevent bias, the experiment should be double-blind. Neither the patients nor the doctor evaluating the patients should know whether each patient received medication.
