Chapter 11-13

When two variables are confounded in an experiment, it means that they are intertwined and their effects on the response variable cannot be distinguished from each other. This makes it impossible for the investigator to determine the individual impact of each variable on the response variable. Therefore, the correct statement is that the investigator cannot separate the effect of the variables on a response variable.

The first study, where the cholesterol levels of long-time niacin takers were compared to those who had never taken niacin, is an observational study because the researchers did not manipulate any variables or assign subjects to specific groups. They simply observed and compared the existing groups. The second study, where subjects were randomly chosen to receive either niacin or a placebo, is a controlled experiment because the researchers manipulated the variable (niacin or placebo) and randomly assigned subjects to the groups.

Blocking is utilized to produce groups that are as similar as possible. Blocking involves dividing participants into subgroups based on certain characteristics or variables that may influence the outcome of the experiment. By doing so, researchers can ensure that each subgroup is represented equally in both the treatment and control groups, making them more comparable. This helps to minimize the impact of confounding variables and increase the internal validity of the study. Blocking is particularly useful when there are known variables that could potentially affect the outcome, allowing researchers to control for these variables and improve the accuracy of the experiment.

The personnel director is performing a census because she is studying the eating habits of all employees at the company, not just a selected group. A census involves collecting data from every member of a population, in this case, all employees. This allows for accurate and comprehensive information about the proportion of employees who buy lunch in the cafeteria, bring their own lunches, or go out to lunch.

The study shows a correlation between studying Latin and higher SAT verbal scores, but it does not prove that studying Latin causes higher scores. There could be other factors (confounding variables) that contribute to the relationship observed. Additionally, the study is limited by self-selection, as students who choose to take Latin may already have certain characteristics that make them more likely to achieve higher scores on the SAT. Therefore, all three statements are true.

This is an experiment because the nutritionist intentionally instructs the players to take a vitamin pill before each game. However, no reasonable conclusion can be made about cause and effect because there is no control group or randomization. Without a control group, it is difficult to determine if the improved performance is solely due to the vitamin pill or other factors. Therefore, while it is an experiment, it does not provide enough evidence to establish a causal relationship between taking the vitamin pill and the team's winning season.

The correct answer is the first option, "The girls at your high school are surveyed to determine if they believe there is any sexual stereotyping in the school newspaper." This qualifies as an observational study because it involves observing and collecting data without any intervention or manipulation of variables. The researchers are simply surveying the girls to gather their opinions and beliefs about sexual stereotyping in the school newspaper.

The given method will not result in a simple random sample of the 348 basketball players because not each group of 58 players has the same chance of being selected. In this method, the players are selected based on their team affiliation, rather than being chosen randomly from the entire pool of players. This means that some players may have a higher probability of being selected if their team has a larger representation in the sample. Therefore, the method does not meet the criteria of simple random sampling.

This design is not a valid stratified design because it does not divide the population into mutually exclusive and exhaustive groups. In this design, the boys and girls are selected separately, but there is no guarantee that every student will be included in one of these groups. A valid stratified design would ensure that every student is assigned to either the boys or girls group, and then random samples would be taken from each group.

This design is an example of a multi-stage cluster sample, as it involves selecting school districts as the first stage and then selecting high schools within each district as the second stage. The population of interest is the set of all high school principals in New England, as the design aims to gather information from these individuals. Not every subset of principals has the same chance of selection, as the design involves simple random sampling at both the district and high school levels. However, results from the interviews can be used to infer responses of the population of interest, as the design aims to gather information from high school principals in New England.