A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?

The correct answer is: It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.

Hint:
We will consider the implication of each of the options and eleminate the wrong options.
Step-by-step solution:-
A. It is likely that all visitors hiked between 4 and 5 miles.
This option states the exact distance hiked by the visitors to be between 4 & 5, which is not suitable because for the mean to be 4.5, the actual distances travelled may be much higher or lower than the mean distance.
∴ This option is eleminated.
B. It is likely that most visitors hiked exactly 4.5 miles.
This option states the exact distance hiked by the visitors to be 4.5, which is not suitable because for the mean to be 4.5, the actual distances travelled may be much higher or lower than the mean distance.
∴ This option is eleminated.
C. It is not possible that any visitor hiked less than 3 miles.
This option states the no visitors could have travelled less than 3 miles, which is not suitable because for the mean to be 4.5, the actual distances travelled may be much higher or lower (even lower than 3 miles) than the mean distance.
∴ This option is eleminated.
D. It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.
This option states that the Actual Mean of the data gathered by the park ranger could be between 4 & 5 miles, which is plausible because the margin of error is 0.5 miles for the mean 4.5 miles. This means that the Actal mean could be between (4.5 - 0.5) miles = 4 miles and (4.5 + 0.5) miles = 5 miles.
∴ This option is correct.
Final Answer:
Option D. i.e. It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles. is the correct Option.