What was the average amount of sleep students in the study got per night?

Question

BlackTom AI · Accepted Answer

The mean reported by the study is 6½ hours (that is, 6 hours 30 minutes).

1) Relevant knowledge points and concepts:
- The arithmetic mean (average) is the sum of all observations divided by the number of observations: mean = (sum of values) / n.
- Units must be consistent; 6½ hours is 6.5 hours or 6 hours 30 minutes.
- Rounding: reported averages are often rounded to the nearest half-hour or tenth as appropriate.

2) Step-by-step reasoning process:
- The study’s summary statistic gives a single central value for nightly sleep across participants; that value is the arithmetic mean.
- Interpreting the provided answer choices, the study’s reported mean must match one of them exactly when converted to the same unit.

3) Calculation example (showing intermediate steps):
- To demonstrate how a mean of 6½ hours could arise, suppose four students slept 6, 6, 7, and 7 hours on average per night.
- Sum = 6 + 6 + 7 + 7 = 26 hours.
- Number of students n = 4.
- Mean = Sum / n = 26 / 4 = 6.5 hours = 6½ hours.
- This calculation shows how the arithmetic mean gives 6.5 hours when the summed total divided by the count equals 6.5.

4) Why the correct answer is correct:
- The study’s reported average corresponds to the arithmetic mean of the sample and is explicitly given as 6½ hours in the answer key. Converting 6½ to decimal gives 6.5 hours, which equals 6 hours 30 minutes, confirming the interpretation of the reported statistic.

5) Why the other options are incorrect:
- 7 hours, 5 hours, and 8 hours are different numerical values and would imply different sums or distributions of sleep data. Unless the summed sleep divided by the number of students equaled 7.0, 5.0, or 8.0 respectively, those choices would not match the study’s reported mean. The answer key specifies 6½ hours, so the other options are not the reported average.

6) Conclusion confirming the final answer:
- Therefore, based on the arithmetic mean interpretation and the study’s reported statistic, the average amount of sleep students in the study got per night is 6½ hours, which matches the provided correct answer.

What was the average amount of sleep students in the study got per night?Single choice

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