Question 1

Three methods for random sampling are: (a) simple random sampling, (b) stratified random sampling, and (c) cluster sampling. In a few sentences, discuss the similarities and differences among these sampling methods. Specifically, what sampling circumstances would lead you to choose each of these methods?

Accepted Answer

The answer of Three methods for random sampling are: (a)...

Question 2

In evaluating an experiment, how would you determine if a variable is an explanatory variable or an extraneous variable?

Accepted Answer

The answer of In evaluating an experiment, how would you...

Question 3

Suppose that two experiments were conducted to compare the effects of two new insect repellants. In Experiment X, a simple random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. In Experiment Y, a stratified random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. (River City has 4 geographic areas of town, the NE, NW, SE, and SW quadrants; 100 people from each quadrant were sampled for Experiment B.)The results of the experiments were the same: fewer insects landed on the arms that had been treated with insect repellant A.
(a)For each experiment, X and Y, discuss whether one can legitimately infer from each of these experiments that repellant A is better than B? Why or why not?
(b)For each experiment, X and Y, discuss whether one can legitimately generalize to the population of River City from each of these experiments? Why or why not?

Accepted Answer

The answer of Suppose that two experiments were conducted to...

Question 4

The likelihood that an animal will successfully avoid a predator's attack should increase if the presence of the predator is detected. Animals are, of course, known to warn others of a predator's presence--the well-known prairie-dog warning call is an example. Some aquatic animals are known to send chemical signals. For example the crayfish and Iowa darter may excrete ammonium from their gills or possibly in their urine during periods of heightened metabolic activity. In an experiment to see if red-legged frogs (Rana aurora) may send or respond to chemical signals, specimens in Oregon were collected as embryos and raised in an aquarium. As tadpoles they were separated into two pairs of aquaria. The "upper tank" in each pair was connected to the "lower tank" to create a (very!) small river. A wooden heron model was placed in one of the upper tanks and moved around for 30 seconds to simulate a predator attack. Both the sender (upper tank) and receiver (lower tank) animals were monitored for added activity (increased movement) indicating antipredator behavior.
(a)What is the explanatory variable (factor) for this experiment?
(b)What is the response variable for this experiment?
(c)During the course of the experiment the investigators were very careful with the wooden heron model not to come in contact with the glass of the aquaria or make noise in any other way. If they had been unsuccessful and their wooden heron made significant amounts of noise, how would that affect the interpretation of the results?

Accepted Answer

The answer of The likelihood that an animal will successfully...

Question 5

Two hundred people who live in San Francisco volunteered to participate in a statistical study. The volunteers were divided into two groups by age, with people under 40 years old in group 1 and people 40 years of age and older in group 2. Those in group 1 were asked to go in for sports once a day for 1 month. Those in group 2 were asked not to go in for sports for 1 month. At the end of the month, progress in weight reduction was significantly higher for group 1 than for group 2. From the resulting data, the researchers concluded that daily sports exercises help every San Francisco resident lose weight faster. Based on the study design, do you think that the conclusions are reasonable?

Accepted Answer

The conclusions are not reasonable because the study did not use random assignment, which is necessary to establish causation. The groups were divided by age, which could introduce confounding variables.

Question 6

Fifty-five people volunteered to participate in a statistical study. For each volunteer, a coin was tossed. If the coin landed tails up, the volunteer was assigned to group 1. If the coin landed heads up, the volunteer was assigned to group 2. Those in group 1 were asked to eat carrot salad daily for 1 year. Those in group 2 were asked not to eat carrot salad for 1 year. At the end of the year, the progress in improving vision was significantly higher for group 1 than for group 2. Did the study use a random selection from some population? Did the study use random assignment to experimental groups? ​

Accepted Answer

The study used random assignment by tossing a coin to decide which group each volunteer would be in, but it did not use random selection because the participants were volunteers, not randomly selected from a larger population.

Question 7

In competitive sports, video recorders have been used more frequently in recent years. The idea behind the recorder is that coaches can replay training sessions for more effective feedback to the athlete. Some people believe video recording may make the athletes more nervous and actually decrease their performance. You have been asked to design an experiment to address this issue for competitive high school tennis players. You have decided to use the accuracy of tennis serves as your response variable, and the number of successful serves out of 100 as your performance measure. The subjects for your experiment are 60 high school male competitive tennis players of varying ability who have volunteered for the experiment.
(a)Describe the treatments in your experiment
(b)One possible confounding variable is the experience levels of the players. Explain how you would control this variable?
(c)Can the results of this experiment be generalized to all male tennis players? Why or why not?

Accepted Answer

The answer of In competitive sports, video recorders have been...

Question 8

One of the tasks of wildlife biologists is to estimate bird populations. One method for doing this is to walk a "transect," typically a long randomly selected rectangle, and count the number of particular species that are seen. During hunting season the biologists wear brightly colored clothes as a protective measure. A theory, known as the "species-confidence hypothesis," predicts that birds may react to these brightly colored clothes. A robin, for example, when confronted with a biologist wearing an orange color may be less afraid than if the biologist were wearing a brown color. The idea is that the orange color gives the robin some "confidence" that the biologist is another (really big!) bird. This is a difficulty because a robin that is less afraid of the biologist may be easier to see and therefore "count" because the robin lets the biologist get closer. This would result in too high an estimate of the robin population. To test this theory a biologist performed a study in her area, wearing a bright orange vest or a brown vest while working. After training herself to accurately estimate distances she indicated on her notes how close the robins would let her get before they flew away (the "approach distance"), using this as a measure of their "confidence." She randomly selected her starting points in each trip through the transects and also carefully noted the weather conditions, specifically the wind speed.
(a)What is the explanatory variable (factor) for this experiment?
(b)What is the response variable for this experiment?
(c)After completing the study the biologist was examining her results and noticed that on those days she wore the brightly-colored vest the wind tended to be of greater velocity. How does this information affect the interpretation of the results of the experiment?

Accepted Answer

The answer of One of the tasks of wildlife biologists...

Question 9

One hundred fifty people who live in Houston volunteered to participate in a statistical study. The volunteers were divided into two groups, with people who have children in group 1 and people who do not have children in group 2. Those in group 1 were asked to eat a lemon slice daily for five months. Those in group 2 were asked not to eat a lemon for five months. At the end of the study it was found that on average, people in group 1 were sick less often than those in group 2. Did the study use a random selection from some population? Did the study use random assignment to experimental groups?

Accepted Answer

The answer of One hundred fifty people who live in...

Question 10

Suppose you want to know how many times per month people of Portland go shopping. You interviewed fifty women from Portland selected randomly. Is the sample likely to be representative of the population of interest?

Accepted Answer

The answer of Suppose you want to know how many...

Question 11

Suppose you want to learn how often students of the Faculty of Arts and Sciences of Harvard University visit the gym. You interviewed students of this faculty with an athletic build. Is the sample likely to be representative of the population of interest? ​

Accepted Answer

The sample is biased because it only includes students with an athletic build, ignoring those who may visit the gym less frequently or not at all, thus not giving every individual an equal chance of selection.

Question 12

The two paragraphs below discuss aspects of two studies, each of which exhibit a bias. For each study, decide whether the problem is selection bias, response bias, or nonresponse bias, and in a few sentences explain why you chose your answer.
(a)One part of the Nurses' Health Study is concerned with possible causes of skin cancer. Nurses were asked about different behaviors and aspects of their health when they entered the study. Then, the nurses were given the questionnaire again if they were diagnosed with cancer. When the questionnaires were analyzed, the investigators discovered that after the nurses were diagnosed with cancer they tended to report a reduced ability to tan. It is thought that the shift in reporting might be caused by an awareness of their diagnosis.
(b)One part of the Demographic and Health Surveys Program is concerned with measures of malnutrition. Investigators measure physical aspects of growing children, and attempt to document the physical characteristics of a population at different ages. Sadly, in some countries many children die early, and thus a bias is introduced in the study when the investigators can not collect the data from the deceased children.

Accepted Answer

The answer of The two paragraphs below discuss aspects of...

Question 13

A common practice of teachers is to have students exchange their quizzes and grade each others. In addition to decreasing the teacher's work load, the reduced time between quiz and feedback is thought to be a plus for learning. Your U.S. History teacher, aware of your statistical prowess, has asked you to design an experiment to test this theory. You have decided to use the mid-term exam (not graded by students) as your response measure. Your history teacher has three classes, one early in the morning, one at noon, and one late in the afternoon. Each class contains 30 students.
(a)Describe the treatments you will use in your experiment
(b)One possible confounding variable is the time of day, since students may be more alert at certain times of the day than at other times. Describe a method would you use to control this variable? (Unfortunately you cannot change the student schedules!)(c)Do you feel the results of your experiment could be generalized to your statistics class? Why or why not?

Accepted Answer

The answer of A common practice of teachers is to...

Question 14

A pharmaceutical company wants to test its new drug that is designed to help balding men grow more hair. From their records of past customers, the company has data on about 5,000 men. The data contains information about the men's hair color, age, and percent of baldness. (A partial list is given below.) For their anticipated experiment, they want to take a sample that is representative of their customers.  ​
(a)Briefly describe how you would select a simple random sample of size n = 20 from this list of customers.
(b)Describe in a short paragraph why you might wish to use a stratified random sample.

Accepted Answer

The answer of A pharmaceutical company wants to test its...

Question 15

Suppose that two experiments were conducted to assess the effect of a new insect repellant. In Experiment A, a simple random sample was taken from the population of River City. In Experiment B, a simple random sample from a group of volunteers from the population of River City was used. The results of the experiments were the same: fewer insects landed on the arms that had been treated with the insect repellant. The volunteers were randomly assigned to the two treatments in both experiments.
(a)For each experiment, A and B, discuss whether one can legitimately infer a cause-and-effect relation between the use of the repellant and fewer insects landing from each of these experiments? Why or why not?
(b)For each experiment, A and B, discuss whether one can legitimately generalize to the population of River City from each of these experiments? Why or why not?

Accepted Answer

The answer of Suppose that two experiments were conducted to...

Question 16

In evaluating an experiment, how would you determine if a variable is an explanatory variable or a response variable?

Accepted Answer

The answer of In evaluating an experiment, how would you...

Quiz 1: Collecting Data in Reasonable Ways

In evaluating an experiment, how would you determine if a variable is an explanatory variable or an extraneous variable?

Suppose you want to know how many times per month people of Portland go shopping. You interviewed fifty women from Portland selected randomly. Is the sample likely to be representative of the population of interest?

Suppose you want to learn how often students of the Faculty of Arts and Sciences of Harvard University visit the gym. You interviewed students of this faculty with an athletic build. Is the sample likely to be representative of the population of interest? ​

In evaluating an experiment, how would you determine if a variable is an explanatory variable or a response variable?

Suppose you want to learn how often students of the Faculty of Arts and Sciences of Harvard University visit the gym. You interviewed students of this faculty with an athletic build. Is the sample likely to be representative of the population of interest?