David conducts his own study. He selects a random sample of 50 students and asks if they are getting 9 hours of sleep per night. Thirty of the 50 students are not getting enough sleep.Does David’s sample result provide convincing evidence that more than 50% of all students at the school are not getting enough sleep?
Answer
A
Yes, it is rare to find a sample result of 0.6 or greater if 0.5 is true. Only 19 out of 200 or a proportion of 0.095 of the simulated random samples are 0.6 or greater.
B
No, it is not rare to find a sample result of 0.6 or greater if 0.5 is true. In fact, 19 out of 200 or a proportion of 0.095 of the simulated random samples are 0.6 or greater.
C
Yes, a sample result of 0.6 proves the population proportion cannot be 0.5.
Explanation
David’s sample proportion is 30 ÷ 50 = 0.6. If half of all students were not getting enough sleep, 19 out of 200 simulated samples—0.095, or 9.5%—still had a sample proportion of 0.6 or greater. That result is not rare enough to provide convincing evidence that more than 50% of students are not getting enough sleep.
AI-written and checked against the verified answer.