Practice: Sampling & Inference

Part A: Random or Biased?

Directions: Determine if each sampling method is RANDOM or BIASED. If biased, explain why.

1. A school wants to know student opinions about the cafeteria food. They survey students waiting in the lunch line.

Circle: RANDOM / BIASED

If biased, why? ________________________________________________

2. A researcher numbers all 800 students 1-800 and uses a random number generator to select 50 students to survey.

Circle: RANDOM / BIASED

3. A TV station asks viewers to call in and vote on their favorite show.

Circle: RANDOM / BIASED

If biased, why? ________________________________________________

4. To study reading habits, a librarian selects every 10th person who enters the public library.

Circle: RANDOM / BIASED

If biased, why? ________________________________________________

5. A principal puts all student names in a box and draws 40 names without looking.

Circle: RANDOM / BIASED

Part B: Making Predictions from Samples

Directions: Use the sample data to make predictions about the population. Show your work.

6. In a random sample of 50 students, 30 prefer online homework over paper homework.

a) What percentage prefers online homework? %

b) If there are 600 students in the school, predict how many prefer online homework:

7. A factory randomly tests 80 light bulbs and finds 4 are defective.

a) What fraction of the sample is defective?

b) If the factory produces 5,000 light bulbs, predict how many will be defective:

8. A random sample of 120 voters shows 72 support a new park. The town has 15,000 registered voters.

a) What percentage of the sample supports the park? %

b) Predict how many voters in town support the park:

9. In a random sample of 200 customers, 140 say they would recommend the store to a friend.

a) What percentage would recommend the store? %

b) If the store has 8,500 customers, about how many would recommend it?

Part C: Which Method is Best?

Directions: Choose the BEST sampling method and explain your choice.

10. A company wants to know what customers think about their service. Which is the best method?

A) Survey customers who file complaints

B) Randomly select 200 customers from the database

C) Survey customers who leave 5-star reviews

D) Ask employees what they hear from customers

Best answer:

Why? ________________________________________________

11. A sports network wants to know Americans' favorite sport. Which sample is LEAST biased?

A) Fans at a baseball stadium

B) People at a shopping mall on Saturday

C) Randomly selected phone numbers across the country

D) Subscribers to a sports magazine

Best answer:

Why are the others biased? ________________________________________________

Part D: Word Problems

12. A random sample of 150 7th graders shows their favorite subjects:

Math: 42 | Science: 36 | English: 30 | Social Studies: 24 | Art: 18

If there are 900 7th graders in the district, predict how many prefer:

a) Math: students

b) Science: students

c) Art: students

13. Two different random samples were taken from the same school about phone usage:

Sample A (n=50): 35 students have smartphones (70%)

Sample B (n=100): 68 students have smartphones (68%)

a) Are these results similar or very different? _______________

b) If the school has 1,200 students, use Sample B to predict how many have smartphones:

c) Why might Sample B be more reliable than Sample A?

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Challenge: Design a Survey

14. You want to know what students at your school think about the length of the school day. Design a sampling method.

a) Population: ________________________________________________

b) How would you select a RANDOM sample? ________________________________________________

________________________________________________

c) What sample size would you use?

d) Give ONE example of a BIASED sampling method for this question:

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