Inferences & Claims From Statistics
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SAT Math › Inferences & Claims From Statistics
In an observational study, people who spent more time outdoors reported higher happiness levels. What can be concluded from the study?
Spending time outdoors causes increased happiness.
Happiness levels are solely determined by outdoor activity.
There is a correlation between outdoor time and happiness.
All happy people spend time outdoors.
Explanation
This question asks what can be concluded from an observational study finding people who spent more time outdoors reported higher happiness. The data shows an association between outdoor activity and self-reported happiness levels. Answer B correctly identifies this as a correlation without claiming causation. Option A inappropriately claims causation, option C makes an absolute statement about all happy people, and option D claims outdoor activity is the sole determinant of happiness. Observational studies can identify correlations but cannot establish that one variable causes changes in another without experimental manipulation and controls.
A study of 200 college students found a positive correlation between the number of hours spent studying and GPA. Which conclusion is most appropriate?
Studying more causes an increase in GPA.
There is an association between studying hours and GPA, but causation cannot be determined.
Students with higher GPAs are more likely to study more.
The more hours a student studies, the higher their GPA will be.
Explanation
This question asks what conclusion is most appropriate from a positive correlation between study hours and GPA. The data shows that students who study more hours tend to have higher GPAs, indicating a positive association between these variables. Answer D correctly identifies that while there is an association, causation cannot be determined from correlational data alone. Options A and C incorrectly claim causation (that studying more causes higher GPA), while option B suggests reverse causation, but none of these causal claims can be supported by correlation data. When dealing with correlational studies, always remember that correlation does not imply causation.
In a study on diet and weight loss, participants who ate less than 1500 calories a day lost weight faster than those who did not. Which limitation affects the conclusion?
The study did not consider exercise habits.
The study proves reducing calories causes weight loss.
The study included only those who wanted to lose weight.
All participants followed the same diet plan.
Explanation
This question asks which limitation affects the conclusion in a diet and weight loss study. The study found that people eating under 1500 calories lost weight faster, but this doesn't account for other factors that might influence weight loss. Answer A correctly identifies that not considering exercise habits is a major limitation, as exercise could be a confounding variable affecting the results. Options B incorrectly claims the study proves causation, option C makes an unsupported assumption about diet consistency, and option D describes participant motivation rather than a methodological limitation. When evaluating study limitations, look for important variables that weren't controlled or measured.
Researchers surveyed 1500 city residents about their exercise habits and health status. Which statement about the data is justified?
Exercise habits are the sole determinant of health status.
There is a correlation between exercise habits and health status.
Regular exercise causes improved health in all city residents.
All healthy residents exercise regularly.
Explanation
This question asks which statement about survey data on exercise habits and health status is justified. The question doesn't specify what the survey found, but based on the answer choices, we can infer it found some relationship between exercise and health. Answer B correctly states there is a correlation, which is the most that can be concluded from observational survey data. Options A and D make causal claims that cannot be supported by survey data alone, while option C makes an absolute claim ('all') that would be nearly impossible to support from any real-world survey. Survey data can reveal associations but not prove causation.
A survey of 500 employees in a company found that job satisfaction is higher among those who work flexible hours. What can be concluded from the study?
Flexible hours cause higher job satisfaction.
There is an association between flexible hours and job satisfaction.
Employees prefer working flexible hours.
All employees who work flexible hours are satisfied with their jobs.
Explanation
This question asks what can be concluded from a survey finding higher job satisfaction among employees with flexible hours. The data shows an association between flexible work arrangements and job satisfaction levels. Answer C correctly identifies this as an association without claiming causation. Option A incorrectly claims causation, option B makes a claim about preferences that wasn't measured, and option D makes an absolute statement ('all') that survey data cannot support. Observational studies like surveys can reveal associations but cannot establish that one variable causes changes in another.
A survey of 1000 adults found that those who drink coffee daily report higher levels of alertness. Which statement about the data is justified?
Coffee is the only factor affecting alertness.
Daily coffee consumption increases alertness.
There is an association between coffee drinking and alertness.
All alert individuals drink coffee daily.
Explanation
This question asks which statement is justified by survey data finding daily coffee drinkers report higher alertness levels. The data shows a relationship between coffee consumption habits and self-reported alertness. Answer B correctly describes this as an association without implying causation. Option A claims that coffee consumption causes increased alertness, option C makes an absolute statement about all alert individuals, and option D claims coffee is the only factor, all of which cannot be supported by observational survey data. Survey findings can reveal associations but cannot prove causal relationships.
A study of 300 people found that those who slept at least 8 hours per night reported feeling more energetic. Which conclusion is most appropriate?
There is a correlation between sleep duration and energy levels.
Sleeping 8 hours makes people more energetic.
Energy levels depend only on sleep duration.
All energetic people sleep at least 8 hours.
Explanation
This question asks for the most appropriate conclusion from a study finding that people sleeping 8+ hours reported feeling more energetic. The data shows an association between sleep duration and self-reported energy levels. Answer B correctly identifies this as a correlation without claiming causation. Option A inappropriately claims that sleeping 8 hours causes increased energy, option C makes an absolute statement about all energetic people, and option D claims sleep is the only factor affecting energy. Observational studies can reveal correlations but cannot establish causal relationships without experimental controls.
Researchers conducted a survey of 200 adults to determine if there is an association between daily coffee consumption and reported levels of stress. The results showed a moderate positive correlation. Which statement is justified by the data?
Drinking coffee increases stress levels.
People who drink more coffee tend to report higher stress levels.
There is no relationship between coffee consumption and stress.
Eliminating coffee will reduce stress for all individuals.
Explanation
This question asks which statement is justified by data showing a moderate positive correlation between coffee consumption and stress levels in 200 adults. The study found an association where higher coffee consumption is linked to higher reported stress levels. Choice B appropriately describes this correlation using "tend to report," which accurately reflects the observational nature of the data without claiming causation. Choice A incorrectly implies causation ("increases"), choice C makes an unsupported intervention claim, and choice D contradicts the finding of a positive correlation. In correlational research, the key is distinguishing between demonstrating an association versus proving a cause-and-effect relationship.
A study focused on 150 teenagers to examine the link between social media usage and sleep quality. The results indicated a strong negative correlation between time spent on social media and sleep quality. What conclusion is most appropriate based on these findings?
Reducing social media usage will improve sleep quality.
Social media is the sole cause of sleep problems.
Teenagers who use social media more tend to have poorer sleep quality.
All teenagers should stop using social media to sleep better.
Explanation
This question asks for the most appropriate conclusion based on a study of 150 teenagers showing a strong negative correlation between social media usage and sleep quality. The data indicates that teenagers who spend more time on social media tend to have worse sleep quality. Choice B correctly describes this relationship using "tend to have," which appropriately reflects the correlational finding without implying causation. Choice A incorrectly suggests a causal intervention effect, choice C claims social media is the only cause of sleep problems, and choice D makes an unsupported universal recommendation. Strong correlations still only demonstrate associations, so avoid language that implies one variable directly causes changes in another.
A research team analyzed data from a sample of 500 people to explore whether owning a pet is linked to lower levels of depression. The study found that pet owners reported lower depression scores on average. What conclusion can be drawn from this study?
Depression can be cured by owning a pet.
Pet owners are less likely to be depressed.
Owning a pet reduces depression levels.
All people should get a pet to lower depression.
Explanation
This question asks what conclusion can be drawn from a study of 500 people showing that pet owners reported lower depression scores on average. The data demonstrates an association between pet ownership and lower reported depression levels in this sample. Choice B correctly states this finding using "are less likely," which appropriately describes the observed pattern without claiming causation or making intervention recommendations. Choices A and C incorrectly imply that pets cause reduced depression or can cure it, while choice D makes an inappropriate universal recommendation based on observational data. When analyzing comparative studies, focus on describing the observed differences between groups rather than inferring causal mechanisms.