Understanding Statistics and Sampling

A class recorded how students get to school: Walk — 8 students, Bus — 12 students, Car — 6 students, Bike — 4 students. How many students are represented in total?

In a class of 30 students, 12 students ride the bus to school. What fraction of the class rides the bus?

A survey asked 20 students what their favorite subject is. The results: Math — 7, Science — 5, English — 4, History — 4. Which statement is supported by the data?

To learn the most popular music genre among all 7th graders in a school, a teacher surveys all students in her music class. Is this sample biased or likely representative?

A school administrator wants to know students' opinions about the cafeteria menu. She randomly selects 40 student names from the school's complete enrollment list and surveys those students. What type of sampling does this describe?

A company posts a survey on its website asking customers to rate its product quality. Customers see the survey and choose whether to respond. Is this sample biased or likely representative of all customers?

A health research team randomly selects $2{,}000$ adults from a national medical registry and finds that those who sleep $7$–$8$ hours per night have fewer health problems. Which best describes the quality of this study's sample?

A student wants to know the favorite color of all 7th graders in her school. She surveys her 5 closest friends and finds that 4 prefer blue. She concludes, 'Blue is the favorite color of 7th graders at our school.' Identify TWO specific problems with her sampling method.

Two surveys are conducted to estimate the percentage of all U.S. adults who exercise regularly:

• Survey A: A magazine emails its online subscribers and gets $5{,}000$ voluntary responses.
• Survey B: A health researcher randomly selects $200$ adults from a national phone registry.

Which survey is more likely to produce a reliable estimate of all U.S. adults?

A candy company tests 100 bags from today's production to check that the candy count per bag is accurate. The   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   is all candy bags produced today. The   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   is the 100 bags that are actually tested.

A PE teacher says, 'To pick 5 students for a fitness demonstration, I randomly chose the first 5 students I saw near the gym door.' Is this true random sampling?

A random sample of 30 students is drawn from a school of 400, where exactly 50% are boys and 50% are girls. The sample contains 18 boys ($60\%$) and 12 girls ($40\%$). Does this mean the sample is biased?

Use the survey information above to answer both parts below.

A toy company wants to know which types of toys children ages 6–12 prefer. They survey children who are waiting in line at a toy store. What is the primary source of bias in this sample?

A city government posts a survey on its website asking all residents to share their opinions about a proposed new park. The survey link is available to anyone who visits the city website. Is this survey likely to represent the opinions of ALL city residents?

A school wants to know whether students support a proposed 10-minute increase to the school day. Two survey designs are proposed:

Design A: Post a sign-up sheet in the library. Any student who wants to share their opinion can sign up and be surveyed.

Design B: Use the school's enrollment list to randomly select 60 students, then survey those specific students.

Which design is more likely to produce a representative sample? Explain using the concept of random sampling and bias.

What error in reasoning is the student making?

What error is the student making in how she reports her finding?

Your school principal wants to know which lunch option is most popular among all 600 students in the school. Design a sampling plan that is likely to produce a representative sample. Your plan must include:

1. The population you are studying
2. How you will select your sample (be specific)
3. Why your method is likely to produce a representative sample

A newspaper headline reads: "New Survey: 90% of People Support Recycling Programs!" The article states that 10,000 people responded to an opt-in online poll on the newspaper's website.

Evaluate this claim. Is the 90% figure likely to be a reliable estimate of all Americans' views on recycling? Identify at least TWO specific problems with the survey design and explain how each could bias the results.