. As a part of their customer-service program, United Airlines wanted to select 10 passengers from today's 9 A.M. Chicago-Tampa flight to be interviewed regarding airport facilities, service, and amenities in the waiting area. Each passenger was given a number on check in, starting with 001 and ending with 250.

a. Describe how you would take a systematic sample of 10 passengers.

b. Describe how you would take a cluster sample of 10 passengers.
c. Describe how you would take a random sample of 10 passengers.
d. Which of the 3 sampling methods would yield the best sample for this application?

Find the definitions of systematic, cluster, and random sampling. One hint: for random sampling, a random number table can be used to choose samples.

a. To take a systematic sample of 10 passengers, you would need to first determine the sampling interval. This can be calculated by dividing the total number of passengers (250) by the number of passengers you want to select (10). In this case, the sampling interval would be 250/10 = 25.

Next, you would randomly select a starting point between 1 and 25. For example, let's say the starting point is 7. From there, you would select every 25th passenger. So you would choose passengers numbered 7, 32, 57, 82, 107, 132, 157, 182, 207, and 232.

b. To take a cluster sample of 10 passengers, you would first divide the passengers into distinct groups or clusters based on a certain characteristic, such as seating area or check-in counter. Then, you would randomly select a certain number of clusters (in this case, 10), and include all the passengers within those selected clusters in your sample.

For example, if there are 10 clusters based on seating areas, you would randomly select 10 of those clusters and include all the passengers seated in those areas in your sample.

c. To take a random sample of 10 passengers, you would assign a unique number to each passenger from 001 to 250. Then, you could use a random number generator or a random number table to choose 10 random numbers between 001 and 250. The passengers corresponding to those randomly generated numbers would be included in your sample.

In this case, you could generate 10 random numbers between 001 and 250, for example: 064, 119, 003, 207, 136, 042, 185, 098, 221, and 150. The passengers with those corresponding numbers would form your random sample.

d. In this scenario, the best sampling method would likely be the systematic sample. This method ensures that every passenger has an equal chance of being selected and provides a representative sample of the entire population. It also allows for a clear and systematic process of selection, making it easier to implement and replicate. The cluster sample may introduce potential bias if the clusters are not representative of the overall population. The random sample, while also valid, might have some practical challenges in terms of actually implementing the random selection process.