Making Inferences and Justifying Conclusions: Evaluating Reports Based on Data (CCSS.S-IC.6)
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Common Core High School Statistics And Probability › Making Inferences and Justifying Conclusions: Evaluating Reports Based on Data (CCSS.S-IC.6)
A health club surveyed 120 high school students at one school about their sleep and screen time last week. The average reported sleep was 6.5 hours per night. Students who reported more than 3 hours of daily screen time also reported less sleep on average. The club concluded that cutting screen time by one hour will make students sleep one hour more.
Which claim is not supported by the data?
The average reported sleep among the surveyed students was 6.5 hours per night.
The survey cannot determine cause-and-effect between screen time and sleep.
These results apply to students at this school and may not generalize to all teens.
Reducing screen time by one hour will make students sleep one hour more.
Explanation
This was an observational, self-reported survey, so a causal, one-to-one effect cannot be concluded. Choices A–C are cautious statements aligned with the reported data and study design.
An online poll on a school club's website asked visitors whether the school should start later. Of 600 responses, 85 percent selected yes. The club reported that most students at the school want a later start time.
Which flaw is present in the reasoning?
The sample is likely not representative of all students because it was an online, self-selected poll.
The poll had too many responses to be useful.
The conclusion should have been about teachers, not students.
A randomized experiment is required to compute a percentage.
Explanation
The poll suffers from selection bias; website visitors who chose to respond may not represent all students. The other options are irrelevant or incorrect statements about surveys.
A teacher offered optional after-school tutoring to two Algebra 1 classes. Of the 50 students, 20 chose to attend tutoring regularly. Their average unit test score was 84, while the 30 students who did not attend averaged 79. The teacher wrote that the tutoring caused students to score 5 points higher.
Which flaw is present in the reasoning?
The sample size is too large to draw any conclusion.
The study uses voluntary participation, so preexisting differences could explain the score gap.
Scores cannot be compared because they are not percentages.
Without a line graph, averages cannot be analyzed.
Explanation
Voluntary participation introduces selection bias; more motivated students may be overrepresented in tutoring. The claim of causation is not justified without random assignment. The other options are irrelevant.