As a part of their customer-service program, United Airlines randomly selected 10 pas-
sengers from today’s 9 A.M. Chicago–Tampa flight. Each sampled passenger is to be
interviewed in depth regarding airport facilities, service, and so on. To identify the sam-
ple, each passenger was given a number on boarding the aircraft. The numbers started
with 001 and ended with 250.
a. Select 10 usable numbers at random using Appendix B.6.
b. The sample of 10 could have been chosen using a systematic sample. Choose the
first number using Appendix B.6, and then list the numbers to be interviewed.
c. Evaluate the two methods by giving the advantages and possible disadvantages.
d. In what other way could a random sample be selected from the 250 passengers?
No "Appendix B.6" shown. Cannot copy and paste here.
a. To select 10 usable numbers at random using Appendix B.6, follow these steps:
1. Open Appendix B.6 (or any other random number generator tool).
2. Set the range from 001 to 250.
3. Generate 10 random numbers within this range.
For example, the generated random numbers could be: 067, 180, 023, 142, 212, 090, 125, 195, 031, 110.
b. To choose the first number using a systematic sample and list the numbers to be interviewed, follow these steps:
1. Determine the sampling interval, which is the total number of passengers divided by the desired sample size. In this case, the sampling interval would be 250/10 = 25.
2. Choose the initial random number between 1 and 25 (inclusive) using Appendix B.6.
3. List the remaining numbers by adding the sampling interval (25) to the initial random number successively until you have 10 numbers.
For example, if the initial random number is 18, the list of numbers to be interviewed would be: 18, 43, 68, 93, 118, 143, 168, 193, 218, 243.
c. Advantages and possible disadvantages of the two methods:
Random Sampling:
Advantages:
- Every passenger has an equal chance of being selected.
- The sample is likely to represent the larger population of passengers accurately.
Disadvantages:
- It may be time-consuming to select the random numbers using Appendix B.6 or other methods.
- There is a small possibility of selecting a sample that is not truly representative of the population.
Systematic Sampling:
Advantages:
- It is a straightforward method that can produce a reasonably representative sample.
- It is less time-consuming compared to randomly selecting individual numbers.
Disadvantages:
- There is potential for bias if there is a pattern in the list of passengers (e.g., passengers with similar last names sitting together).
- If the initial random number is chosen poorly, the sample may not be as representative.
d. Another way to select a random sample from the 250 passengers could be to use a computer-based random number generator. Many statistical software packages, as well as spreadsheet programs like Microsoft Excel, have built-in functions that can generate random numbers. By specifying the range (001-250) and the desired sample size, the software can generate the random sample efficiently. The advantage of this method is that it eliminates the need for a manual random number selection process, making it quicker and potentially more precise.
a. To select 10 usable numbers at random using Appendix B.6, you would need to refer to the specific appendix mentioned. Without access to Appendix B.6, it would not be possible to provide you with the exact list of numbers.
b. For selecting a systematic sample, you would follow a specific pattern in choosing the numbers. To do this using Appendix B.6, you would start by selecting the first number randomly from the table. Let's say the first number chosen was 023. Then, you would proceed by choosing every 25th number from the table, since there are 250 passengers and 10 numbers need to be selected. So, you would select numbers 023, 048, 073, 098, 123, 148, 173, 198, 223, and 248.
c. Advantages of random sampling:
- Random sampling ensures that each passenger has an equal chance of being selected, which increases the representativeness of the sample.
- It reduces bias and ensures fairness in the selection process.
Disadvantages of random sampling:
- It might be time-consuming and cumbersome to generate random numbers for large populations.
- Random sampling may result in a sample that is not proportionally representative of different subgroups within the population.
Advantages of systematic sampling:
- It is relatively easier to implement compared to random sampling, especially when dealing with large populations.
- Systematic sampling provides a uniform spread across the population, ensuring coverage of different subgroups.
Disadvantages of systematic sampling:
- Systematic sampling may introduce bias if there is a pattern or periodicity in the population.
- It may not capture the full variability within the population if there is clustering or other patterns in the data.
d. Another way to select a random sample from the 250 passengers could be to use a random number generator. You could generate 10 random numbers within the range of 001 to 250, ensuring that each number is unique and that all passengers have an equal chance of being selected.