Question

In 1984 the country of Morocco in an attempt to determine the average amount of time that tourists spend in that country on a visit tried two different sampling procedures. In one, they questioned randomly chosen tourists as they were leaving the country; in the other, they questioned randomly chosen guests at hotels. (Each tourist stayed at a hotel.) The average visiting time of the 3000 tourists chosen from hotels was \(17.8\), whereas the average visiting time of the 12,321 tourists questioned at departure was \(9.0 .\) Can you explain this discrepancy? Does it necessarily imply a mistake?

Short answer

The discrepancy between the two results can be attributed to the selection bias present in the second sampling method, which involved questioning hotel guests. Hotel guests may stay longer on average compared to other tourists, resulting in a higher average visiting time found in their sample. It does not necessarily imply a mistake in the calculations, but rather a limitation or difference in the two sampling methods used. To make a more accurate conclusion about the average visiting time, it would be helpful to combine both sampling methods or to use a more representative method that minimizes selection biases.

Step-by-step solution

Examine the first sampling procedure

The first sampling procedure involved questioning randomly chosen tourists as they were leaving the country. This method can be assumed to provide a good representation of the average visiting time, as it includes tourists who just left and covers a broad range of visiting times.

Examine the second sampling procedure

The second sampling method involved questioning randomly chosen guests at hotels. This method may not provide a good representation of the average visiting time, as it could have a selection bias. The people staying at hotels may be more likely to stay for longer periods of time, as they are possibly on vacation or in a more privileged position to travel.

Identify possible biases or issues in the sampling methods

Comparing the two sampling methods, it seems that the second method may have a selection bias that would result in a higher average visiting time. People staying at hotels are not necessarily representative of all tourists. Furthermore, the number of hotel guests is considerably smaller than the number of tourists questioned at departure (3,000 vs. 12,321), which could affect the average.

Explain the discrepancy

The discrepancy between the two results can be likely attributed to the selection bias present in the second sampling method. Hotel guests may stay longer on average compared to other tourists, resulting in a higher average visiting time found in their sample. It does not necessarily imply a mistake in the calculations, but rather a limitation or difference in the two sampling methods used.

Conclude if there is a mistake or not

The discrepancy between the two averages does not necessarily imply a mistake in the procedures themselves, as both averages were calculated from their respective samples. However, it highlights the importance of understanding the potential biases and limitations inherent in the sampling methods used. To make a more accurate conclusion about the average visiting time, it would be helpful to combine both sampling methods or to use a more representative method that minimizes selection biases.