Exam 1: Collecting Data in Reasonable Ways

The most basic sampling method studied in statistics is the simple random sample (SRS). In your own words, what is the correct definition of a simple random sample of size n?

A researcher wishes to study the relationship between the level of background noise and mental concentration. The treatment (noise level) will have three levels: no noise, low-intensity noise, and high-intensity noise. the subjects are to be divided into three groups, and each group is to receive one of the treatments. He has available to him a set of 60 female volunteers and a set of 90 male volunteers. What experimental design strategy would help him eliminate the introduction of gender as a confounding variable? ​

Which of the following best summarizes "nonresponse bias"? ​

Briefly describe how populations and samples differ.

A control group provides a baseline for comparison to a treatment group.

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?

In a well-designed experiment, the factors are confounded whenever possible.

If the subjects as well as the person measuring the response are aware of the treatment assigned to the subject, only single-blinding is being used.

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?

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?

The ZZZ chain of motels has a standard method of constructing their rooms to maximize the ease of parking for its customers. The rooms are arranged in adjacent buildings so that each customer can park outside the rented room. The layout for one of the hotels with 48 rooms located along a famous highway is diagrammed below: Route 66 ​ ​ The manager would like to survey customers in 12 of his rooms (one randomly selected customer for each room selected in the sample) to assess their satisfaction with the motel services. The surveys will be placed on the customers' beds before they check in to the motel. In order to make the directions easy to follow, he elects to use systematic sampling. (a)Explain how you would use random numbers to set up the systematic sampling process. (b)Write a short paragraph for the maids that helps them carry out your method in part (a).

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?

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?

A study is an observational study if the investigator observes the behavior of a response variable when one or more factors are manipulated.

Which of the following best describes the meaning of "variable confounding"? ​

The method of control wherein an extraneous variable is held constant is called blocking.