Mrs. Carlson has discovered that the students in her class who watch a larger amount of television do more poorly on her exams compared to those who watch a smaller amount of television. Which of the following conclusions can Mrs. Carlson draw? Explain your answer.
a. Watching television causes students to do poorly on her exams.
b. Watching television causes students to spend less time studying, and the fact that they spend less time studying causes these students to do more poorly on the exams.
c. Doing poorly on exams causes students to watch television more frequently.
d. All of the above are probably valid.
e. None of the above conclusions is valid.
The correct answer is (b) Watching television causes students to spend less time studying, and the fact that they spend less time studying causes these students to do more poorly on the exams.
This conclusion can be drawn based on the information provided. Mrs. Carlson has observed a correlation between watching a larger amount of television and doing more poorly on exams. However, correlation does not imply causation. It is possible that other factors, such as study habits or motivation, are influencing both television-watching behavior and exam performance.
Option (a) is not a valid conclusion because it assumes a causal relationship between watching television and poor exam performance without considering other potential factors.
Option (c) is not a valid conclusion because it suggests that doing poorly on exams causes students to watch television more frequently, which is not supported by the information given.
Option (d) is not a valid conclusion because only option (b) considers other potential factors that may be influencing the relationship between television-watching behavior and exam performance.
Therefore, the correct conclusion is (b).
To determine the correct conclusion, Mrs. Carlson needs to consider the potential cause and effect relationship between watching television and doing poorly on exams. Let's evaluate each option:
a. "Watching television causes students to do poorly on her exams."
Mrs. Carlson could draw this conclusion if she conducted an experiment where she randomly assigned students to watch different amounts of television and observed a clear cause-and-effect relationship between watching television and exam performance. However, based on the information given, Mrs. Carlson can't definitively state that watching television directly causes poor exam performance.
b. "Watching television causes students to spend less time studying, and the fact that they spend less time studying causes these students to do more poorly on the exams."
This conclusion seems more plausible based on the information provided. Mrs. Carlson could reasonably assume that watching television leads to a reduction in study time, which subsequently affects exam performance. By drawing this conclusion, she acknowledges that there may be other variables at play, such as motivation or other study habits.
c. "Doing poorly on exams causes students to watch television more frequently."
This conclusion is not supported by the information given. It assumes that poor exam performance drives students to watch more television. While this could be a possibility, the initial statement and data provided do not support this conclusion.
d. "All of the above are probably valid."
While option b seems like the most reasonable conclusion based on the information provided, we cannot say with certainty that option a or c are valid. Therefore, Mrs. Carlson cannot draw the conclusion that all of the above options are valid.
e. "None of the above conclusions is valid."
Considering the explanations above, this option seems to be the most accurate. Mrs. Carlson cannot definitively conclude that watching television directly causes poor exam performance (option a) or that poor exam performance causes students to watch more television (option c). However, option b provides a reasonable explanation based on the given information.