Objectives

After completing this assignment, you should be able to:

• Think about the nuances involved in random versus nonrandom sampling procedures.
• Combine your knowledge of sampling with the practicalities present in real life situations.
• Debate using one type of sampling procedure over another, weighing the pros and cons of each one.

Instructions

Use the following scenario to complete the following task and answer the assignment questions:

The Illinois Bureau of Tourism would like to obtain some specific information about how its I-74 welcome center is being used. The management would like an estimate of how many visitors came to this welcome center in the past month (August, 2021). They have the funds to hire observers to count the number of visitors for a total of 24 hours of observation. Propose a sampling plan to identify which days/hours the counter will be stationed at the welcome center entrance. Assume the population is the 372 daylight hours in August- 12 daylight hours from 8 am to 8 pm during the 31 days in August. In 2021 there will be 9 weekend days (Saturday/Sunday) and 22 weekdays in August. You will need to choose a sample of 24 hours from this population. Note that the sampling unit here is the hour (not the individual visitor). Determine which 24 1-hour time periods to make observations in order to have a representative sample of time periods in August. Indicate the days and times you would schedule the observations.

Use the following approaches to generate a sample:

1. "Judgment" Sample. First, use your judgment to choose 24 time periods that will be representative of the 372 daylight hours in August. Think of the 24 days and times that you would sample, based on your best judgment on what might be representative time slots.
2. Simple Random Sample. Now generate a simple random sample. Use an online random number generator. Note that you will first need to number all of your possible dates/times, and then ask the online program to generate 24 random numbers for you. Match these with the dates/times on your list.

Any of the following are easy to use free online random number generators:

• www.random.org/integersLinks to an external site.
• www.randomizer.orgLinks to an external site.
• www.pangloss.com/seidel/rnumber.cgiLinks to an external site.

Answer the following questions about your simple random sample:

What do you think of the days/times that resulted – how do these compare to those you proposed by using your own judgment?

Is the sample size of 24 observations adequate to provide useful information about use of the welcome center? (Use one of the online sample size calculators to help you answer this question – see "Determining Sample Size.")

Do you think this sample would yield an accurate estimate of use if we calculated the average use per hour from the 24 observations and multiplied by 372 to expand to all daylight hours in August?

Do you see any biases in the sample? If so, what biases do you see?

1. Stratified Sample. In most time sampling situations like this, you can use a stratified sample to assure a good sample distribution across times of day and days of the week.
2. Use the following six strata for a stratified sample. Then use simple random sampling to choose four hours/dates within each strata.

• Weekdays (M-F) 8-11 am
• Weekdays 12-3 pm
• Weekdays 4-7 pm
• Weekends (Sa-Su) 8-11 am
• Weekends 12-3 pm
• Weekends 4-7 pm

1. General Comments
2. How might the Illinois Bureau of Tourism use a nonrandom sampling technique to collect the information they are seeking? What would be the drawbacks, if any, of using this approach?
3. Which approach do you think yields the best sample for this problem? Why?

4. How might the Illinois Bureau of Tourism use a nonrandom sampling technique to collect the information they are seeking? What would be the drawbacks, if any, of using this approach?

5. Which approach do you think yields the best sample for this problem? Why?