Approximately of the teens in the study who are classified as heavy texters are not really heavy texters.
It is not possible that the percent of all US teens who are heavy texters is less than .
The percent of all US teens who are heavy texters is .
It is doubtful that the percent of all US teens who are heavy texters is .
Explanation
Correct answer: D.
Choice D is correct. The given margin of error of indicates that the actual percent of all US teens who are heavy texters is likely within of the estimate of , or between and . Therefore, it is unlikely, or doubtful, that the percent of all US teens who are heavy texters would be .
Desmos solution:
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Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. The margin of error doesn't provide any information about the accuracy of reporting in the study.
Choice B
Choice B is incorrect. Based on the estimate and given margin of error, it is unlikely that the percent of all US teens who are heavy texters would be less than , but it is possible.
Choice C
Choice C is incorrect. While the percent of all US teens who are heavy texters is likely between and , any value within this interval is equally likely. We can't be certain that the value is exactly .
Student discussion
marcosat 2 likes
Guys I actually learned what the margin of error means. Imagine we have a universe where there are only 100 people. We do a randomized survey to measure feet size. The model says that the average feet size is 4 units. However, as we only tested 10 people, the margin of error could be reasonably high. Picture this, of the 100 people, we had terrible bad luck and we surveyed the people with the biggest feet. Our model would be far from the turth when we include the whole universe. That's the reason why margin of error decreases as sample size increases. Moreover, it does not tell you anything about the accuaracy of the survey, it's just a potential flaw in future predictions tied to you original sample.