Data Collection Basics
A teacher wants to know how many hours students at her school spend playing video games each week. Is this a statistical or non-statistical question?
Statistical. The answers will vary from student to student
A student posts a poll on Instagram asking followers whether they prefer school uniforms. People choose whether or not to respond. What type of sample is this? Will the results be biased? Why or Why not?
Voluntary response sample.
Yes they will be biased b/c the student will get responses only from people with strong opinions.
A restaurant asks customers who are currently eating there to rate the restaurant. What type of bias could occur because people who don't eat there are excluded?
Undercoverage bias. People who don't visit the restaurant are not represented.
What does SRS stand for?
Simple Random Sample.
A researcher wants to know whether drinking coffee helps students perform better on tests. She randomly assigns half of the students to drink coffee before a test and the other half to drink water. Is this an experimental or observational study?
Experimental b/c there is a treatment.
A school surveys 75 randomly selected seniors to determine how many hours seniors spend studying each week. Identify the population and the sample.
Population: All seniors at the school.
Sample: The 75 seniors surveyed.
A teacher wants to find out how the studnets at the high school feel about the lunch menu. She surveys the first 15 students who walk into her classroom to find out what students think about the school lunch menu. What type of sample is this? Does it cause bias? Why or why not?
Convenience Sample
Yes it causes bias b/c it does not represent the while population of high school students.
A survey asks, "Don't you agree that our school's new schedule is terrible?" What type of bias is this?
Response bias. The wording of the question is leading and may influence people's answers.
You want to randomly select 10 students from a school of 500 students using a random number table. What numbers should you assign to the students (be specific).
001-500
A survey of 100 randomly selected people finds that 72% own a pet. Would you expect a different random sample of 100 people to give exactly 72%? Explain.
Not necessarily. Different random samples will produce different results because of sampling variability.
A researcher wants to know the average number of hours teenagers spend on social media. She surveys every teenager in the United States. What is this called?
A census.
A principal assigns every student in the school a number from 1 to 1,200 and uses a random number generator to select 100 students. What type of sample is this? Does it cause bias, why or why not?
Simple Random Sample (SRS)
It does not cause bias because every student has the potential to be chosen for the sample.
A school randomly selects 100 students to complete a survey. However, 70 students never return the survey. What type of bias is this?
You are using a random number generator to select 5 students from a list of 30 students. The generator gives you the numbers 4, 12, 12, 19, and 30. What should you do with the repeated 12?
Ignore the repeated 12 and generate another number because each student can only be selected once.
A school surveys randomly selected students to determine the average amount of money students spend on lunch each week. Should the select 25 students or 100 students for the most accurate results. Why?
100 students because increasing the sample size decreases sampling variability, so the estimates are more likely to be closer to the true population mean
The principle notices student absences are going up. She asks a SRS of 100 students who many days they have been absent and what their grades are for the year.
What is the statistical questions she is trying to answer?
Does the number of absences a student have impact their grade?
A researcher wants to select 5 students randomly from a list of 200 students. She puts each student's name on an identical piece of paper, mixes them in a hat, and draws 5 names. Why must the pieces of paper be identical?
So every student has an equal chance of being selected. Different-sized or shaped papers could make some names easier to select than others.
A company surveys people about their favorite brand of athletic shoes by standing outside a Nike store. Which direction would you expect the results to be biased? Explain.
The results will likely overestimate the popularity of Nike because people shopping at Nike are more likely to prefer Nike shoes.
Why do we want to collect a sample randomly?
To avoid bias.
A researcher wants to know the percentage of students who have a part-time job. She surveys 50 randomly selected students and finds that 64% have a job. Is 64% guaranteed to be the true percentage for the entire school? Explain.
No. The sample percentage is an estimate of the population percentage. Different samples will produce different results due to sampling variability.
A researcher randomly divides students into two groups. One group gets to listen to music while studying, and the other group studies in silence. The researcher compares their test scores. Is this an observational study or an experiment? Explain.
Experiment. The researcher imposes a treatment (listening to music) on one group and compares the results.
You want to select 5 students from this class of 26 students to take sample and give a survey to. Describe the steps for using a random number generator to create your list of 5 students.
1) Assign every student a number 1-26
2) Use a random number generator to select 5 random numbers 1-26.
3) Select the 5 students that are assigned to each of those numbers.
4) Survey those five students.
A researcher wants to determine what percentage of adults exercise regularly. She conducts a telephone survey, and 95% of respondents say they exercise regularly. However, when researchers observe people at a gym, they find that only 60% of people in their study exercise regularly. What type of bias might explain the difference, and why?
Response bias. People may be more likely to say they exercise regularly when answering a survey than they are to actually do it.
You are selecting 3 stores from a list of 21 stores using a random number table. Use the table below to select the 3 numbers for the stores.
32962 09101 97180 92314 32910 89321
20 , 01 , and 18
A movie theater wants to know what time customers prefer evening movies to begin. It surveys 100 randomly selected customers who attend the 7:00 p.m. show. What role does undercoverage bias have in this sample?
People who attend other showtimes, or who do not attend the 7:00 p.m. show, are not represented. The theater should use an SRS of its entire customer population rather than only surveying customers at one showtime.