Making Samples
A teacher has 30 students and wants an SRS of 5. Describe how the teacher could select the sample.
Number the students 1–30 and use a random number generator to select 5 different numbers.
What does SRS stand for?
Simple Random Sample
A teacher numbers all 30 students in her class and uses a random number generator to select 6 students. What sampling method is this?
SRS!
A radio station asks listeners to go to its website and vote on whether they like a new morning show. What type of sample is this?
What U.S. state capital shares its name with the most populated city in South Carolina?
Charleston
A company has employees in Sales, Marketing, Finance, and HR. Describe how to take a stratified random sample.
Randomly select employees from each of the four departments.
A researcher uses systematic sampling by selecting every 15th person on a list for a study, and begins with their friend who is name #15. What important step did the researcher forget?
The initial person was not randomly selected.
A school surveys every 20th student who enters the building in the morning. What sampling method is this?
Systematic Random Sample!
A grocery store manager wants customer feedback, so she surveys the first 30 customers she sees near the checkout lanes. What type of sample is this?
What is the longest river in the United States?
Missouri River
A school has 40 homerooms. Describe how to take a cluster sample of students using the homerooms as clusters.
Randomly select some homerooms and survey every student in the selected homerooms.
A researcher says, “Stratified and cluster sampling are basically the same because both divide the population into groups.” Explain why this statement is incorrect.
Stratified sampling randomly selects some individuals from every group, while cluster sampling randomly selects entire groups and includes everyone in those selected groups.
A district randomly selects 4 entire classrooms and surveys every student in those classrooms. What sampling method is this?
Cluster Sample
A sports website posts a poll asking visitors to rate a controversial referee call. Why might the results be biased?
It is a voluntary response sample; people with stronger opinions about the call may be more likely to respond.
Which blood type is known as the universal donor for red blood cells?
A hospital has 1,200 employees divided among 6 departments. The hospital wants a stratified random sample of 60 employees, with the same number selected from each department. Describe exactly how the sample should be selected. sample using an appropriate sampling method.
Divide the employees into the 6 departments. Randomly select 10 employees from each department, giving a total sample of 60 employees.
A teacher wants an SRS of 5 students from a class of 25. She writes the students’ names on identical slips of paper, mixes them, draws one name, puts it back, mixes again, and repeats until she has drawn 5 names. Explain what is wrong with her method.
She should not replace selected names because the same student could be selected more than once. An SRS of 5 requires 5 different students.
A company has employees working in five different departments. It randomly selects several employees from every department rather than randomly choosing entire departments. What sampling method is being used?
Stratified Random Sample
A streaming service wants to estimate how many hours Americans spend watching TV each week but surveys only people with an active streaming subscription. Identify the bias and explain the problem.
Undercoverage; people without streaming subscriptions cannot be selected and may have different viewing habits.
What is the smallest country in the world by area?
Vatican City
A music festival expects 12,000 attendees and wants a systematic random sample of 400 people as they enter the festival. Describe exactly how the organizers should select the sample, including how they determine the interval and starting point.
Calculate 12000/400 = 30. Randomly select a number from 1–30 as the starting point. Select that person and then every 30th person after them until 400 people have been selected.
A city is divided into neighborhoods. Each neighborhood contains a similar mixture of ages, incomes, and family sizes. Researchers want a representative sample while minimizing the time and cost of traveling throughout the city. Would stratified or cluster sampling be more appropriate? Explain.
Cluster sampling. Randomly selecting a few neighborhoods and surveying everyone within them can reduce travel while the selected clusters can still reflect the varied population.
A school wants to estimate student satisfaction with school lunches. Students’ opinions tend to differ greatly by grade level, but students within the same grade tend to have similar opinions.
Would it be better to use a stratified random sample by grade level or a cluster sample by grade level? Explain why.
Stratified random sample. Since opinions differ among grade levels, the school should randomly sample students from every grade so that each grade is represented.
A gym randomly selects 300 members and asks, “Considering the serious health risks associated with inactivity, how many days per week do you exercise?” Only 90 members respond. Identify two potential sources of bias and explain each.
Nonresponse because 210 selected members didn't respond, and response bias because the wording could influence people to report exercising more than they actually do.
Which former European country split peacefully in 1993, known as the Velvet Divorce, forming two new countries, one of which becoming the ***** Republic?
Hint: The country’s name combined the names of the two countries that separated.
Czechoslovakia!