Which statement is best supported by these results?

Question

A researcher surveyed 200 randomly selected students at a large high school and asked how many hours of sleep they got on a typical school night. The mean of the sample was 7.1 hours, with an associated margin of error of 0.3 hours.

Accepted Answer

B. It is plausible that the mean sleep time of all students at the school is between 6.8 and 7.4 hours.. A margin of error describes a plausible range for a population value, not for individuals. The sample mean is 7.1 and the margin of error is 0.3, so the plausible interval for the mean sleep time of the whole school is 7.1 - 0.3 = 6.8 to 7.1 + 0.3 = 7.4 hours.

Answer

A. Every student who was surveyed sleeps between 6.8 and 7.4 hours on a typical school night. — The interval describes the population MEAN, not each individual. Plenty of surveyed students will sleep far outside 6.8-7.4 while the average still lands inside it.

Answer

C. Exactly 95% of the students at the school sleep between 6.8 and 7.4 hours. — This turns the confidence level into a percentage of students. The interval is about where one number — the population mean — plausibly sits, not about how many students fall in a range.

Answer

D. The mean sleep time of all students at the school is exactly 7.1 hours. — 7.1 is the mean of the 200 students sampled, not of the whole school. The margin of error exists precisely because the population mean is probably near 7.1 rather than exactly 7.1.

Problem-Solving and Data Analysis practice question

Answer: B. It is plausible that the mean sleep time of all students at the school is between 6.8 and 7.4 hours.

Why the other answers are wrong

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