AP Stats: Experimental Design and Sampling Design
Systematic Random Sample
A sample where every nth individual is selected from a list or queue.
The owner of a plant nursery will conduct a study to investigate whether a new fertilizer is more effective than an older fertilizer in helping the growth of young tomato seedlings. The owner selects a simple random sample of 50 young tomato seedlings from all the young tomato seedlings in the nursery. Half of the selected seedlings will be randomly assigned to receive the new fertilizer, and the remaining seedlings will receive the older fertilizer. The growth of the seedlings will be recorded for the next month. What is the main reason in the study for selecting a simple random sample from the population? A. The simple random sample allows the researcher to establish a causal relationship among the treatments. B. A simple random sample selected from the population allows the results to be generalized to the population. C.A simple random sample should be used to obtain all experimental units D.A simple random sample allows for the random assignment of treatments to experimental units.
B
A scientist studying soil acidity collected soil samples from a plot of land with a stream running through it. The soil samples came from land located on only one side of the stream. What is the potential source of bias that might result from the sampling method? A.Response Bias, where the question wording is leading or confusing B.Response Bias, where responses are self-reported C.Nonresponse bias D. Undercoverage bias
D
An experiment compared the adhesion of 2 types of paint, A and B, to 3 types of metal, 1, 2, and 3, used in automobiles. Thirty sheets of metal were used in the experiment: 10 of Metal 1, 10 of Metal 2, and 10 of Metal 3. Half of each metal type will receive paint A and the other half will receive paint B. The adhesion of the paints was measured, and the measures were compared. How many experimental units are in the experiment? A. 2 B. 3 C.10 D.30 E. 60
D
SRS disadvantages
Large variance, may not be representative, must have sampling frame
Cluster Advantages
Unbiased, cost is reduced, sampling frame may not be available
SRS Advantages
Unbiased, easy
Sampling frame
a list of individuals from whom the sample is drawn
Stratified Random Sample
a sampling design in which the population is divided into several subpopulations, and random samples are then drawn from each stratum
Treatment
a specific condition applied to the individuals in an experiment
Cluster Disadvantages
may not be representative of population
Response Variable
measures an outcome of a study
Completely Randomized Experiment
one in which a random process is used to assign each individual to one of the treatments
Sample
part of a population
Replication
repeating the essence of a research study, usually with different participants in different situations, to see whether the basic finding extends to other participants and circumstances
Double-Blinding
the act of blinding both the subjects of an experiment and the researchers who work with the subjects
Sampling Design
the method used to choose the sample from the population
Census
the official count of a population
experimental units
the smallest collection of individuals to which treatments are applied
Levels
the specific values that the experimenter chooses for a factor
Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment? A. Students should not have been randomly selected B.The treatments (new menu item) were not randomly assigned to the students. C. There was no replication because students did not eat both menu items. D.An item that is currently on the menu should have been used as a control.
B
Stratified disadvantages
Difficult to do if you must divide stratum, formulas for SD in confidence intervals are more complicated, need sampling frame
Population
Entire group of individuals that we want information about.
Stratified advantages
More precise unbiased estimator than SRS, less variability, cost reduced if strata already exists
A certain company has five departments, A, B, C, D, and E. The number of employees in each department is 10, 10, 20, 30, and 30, respectively. A sample of 10 employees from all employees will be selected. Of the following descriptions of sampling procedures, which is most likely to introduce a potential source of bias? A. Randomly select 10 employees from department C B. Randomly select 1 employee from each of A and B, 2 employees from C, and 3 employees from each of D and E C. Randomly select every tenth employee from a randomized list of names of all employees D. Randomly select 10 employees from all 100 employees
A
A professor at a large university plans to conduct a study to compare the effect of online texts versus regular printed texts on student learning. If the findings are to be generalized to all students at the university, which of the following must be part of the design? A. The students in the study should be a random sample from the population of students at the university. B. The students in the study should have experience using online and regular texts. C. The students should be allowed to choose which type of text they would like to use so that different learning styles are taken into consideration. D.The professor should collect data from all students in the population before generalizing results.
A
A researcher conducted an experiment to investigate the effectiveness of a medicated lotion in treating a skin irritation. A group of 80 people with a history of skin irritation volunteered for the study. Of the 80 people, 40 were randomly assigned the medicated lotion, and the remaining 40 were given a nonmedicated lotion. At the end of one month, the skin irritation had cleared for 36 people (90 percent) using the medicated lotion and 16 people (40 percent) using the nonmedicated lotion. Analysis of the results showed the difference was statistically significant. What can be concluded from the experiment? A.Of the people whose skin irritation cleared, the difference between the two groups was only 20 people, which is too small for a generalization. B.There is enough evidence to conclude that the medicated lotion is more effective than the nonmedicated lotion in treating the skin irritation. C. Any conclusion is problematic because the participants were volunteers and were not randomly selected from the population. D. There was no difference in the effectiveness of the two lotions because 28 people still had the skin irritation.
B
Which of the following is a benefit to using a random sample for an observational study? A. The distribution of the sample will not match the distribution of the population. B. The results of the observational Study can be generalized to the population. C. A casual Relationship can be determined. D. A random sample is the easiest method of data collection.
B
A researcher conducted a study investigating the effect of computer screen time on a person's amount of REM sleep. The researcher randomly assigned 100 people into four groups. The first group was given 2 hours of computer screen time each day, the second group was given 4 hours each day, the third group was given 6 hours each day, and the fourth group was given 8 hours each day. The study was conducted for one week, and the amount of REM sleep for each person was measured. What is the explanatory variable in the study? A. The four groups in the study B. The 100 people in the study C.The amount of REM sleep D.The amount of computer screen time
D
confounding variable
a factor other than the factor being studied that might influence a study's results
Matched Pair Experiment
each case gets both treatments in random order and we examine individual differences in the response variable between the two treatments
Randomized Block Experiment
individuals are first sorted into blocks, and then a random process is used to assign each individual in the block to one of the treatments
Blinding
method used so that units do not know which treatment they are getting
Systematic disadvantages
not representative, can be confounded by trend
Observational Study
observes individuals and measures variables of interest but does not attempt to influence the responses
Cluster Sample
obtained by selecting all individuals within a randomly selected collection or group of individuals
Simple Random Sample (SRS)
of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected
Systematic advantages
unbiased, no sample frame, ensures sample is spread throughout population.
