Algebra 1 Glencoe McGraw-Hill JoAnn Evans

1. Math 8H 12-1 Sampling and Bias Algebra 1 Glencoe McGraw-Hill JoAnn Evans

2. A random sample is a set of items that are chosen from a population in such a way that each time an item is selected, every item in the population has an equal opportunityto appear in the sample. A random sample must be representative of the population and chosen without preference.

3. 150 passengers on an airplane are each assigned a different number from 1-150. Five of the 150 numbers are chosen at random to get a free flight coupon. A simple random sample is a sample that is as equally likely to be chosen as any other sample from the population. Simple Random Sample 150 passengers are divided into 2 groups by gender. Two passengers are randomly selected from each of the two groups to get a free flight coupon. A population is first divided into similar, non-overlapping groups. A simple random sample is chosen from each group. Stratified Random Sample Items are selected at specified times or intervals from the population. Systematic Random Sample Every 30th passenger to board the plane is given a free flight coupon.

4. Ten students are going to be chosen from each class at Thousand Oaks High School to be on an advisory committee with the principal. What is the population in this case? The population is the entire student body of TOHS. What is the sample? The sample is 4 groups of 10 students: 10 freshman, 10 sophomores, 10 juniors, and 10 seniors. This is a stratified random sample. The population is divided into non-overlapping groups, then a random sample will be chosen from each group.

5. A clothing company wanted to check the quality of the jeans it produced. Instead of inspecting each and every pair of jeans, the manager decided to inspect every fourth pair that was produced. What is the population in this case? The population is the jeans made by the company. What is the sample? The sample is every 4th pair of jeans that is produced. This is a systematic random sample. The population of jeans to be chosen will be at regular intervals (every 4th pair that is made).

6. Mrs. Lowe chooses students to pass out snacks each day in her kindergarten class. Each of her 20 students’ names are written on a small piece of paper, placed in a cup, and mixed up. She pulls out 4 names to be snack helpers. What is the population in this case? The population is Mrs. Lowe’s kindergarten class. What is the sample? The sample is four students. This is a simple random sample. Each student is equally likely to be chosen as a snack helper for the day.

7. Biased vs. Unbiased Samples Remember, a random sample is considered to be representative of the entire population it’s drawn from and is chosen without any preference (favor). A random sample is considered, therefore, to be unbiased. It is impartial and without favoritism. In contrast, a biased sample will favor one or more parts of the chosen population over others.

8. A hospital’s administration is interested in opening a gym for all its employees. They ask each member of the night-shift emergency room staff if he or she would use a gym, and if so, what hours the employees would prefer to use it. Sample? The night-shift staff of the hospital Population? All hospital employees Biased? Unbiased? Why? Biased; Since they all work the night shift, their idea of hours the gym should be open will be hours convenient for their schedule.

9. Every tenth customer in line at the Human Bean Coffee Shop is asked what their favorite beverage is. Sample? Every 10th customer Population? All customers of the Human Bean Biased? Unbiased? Why? Biased; Customers who go to this coffee shop may be biased in favor of the drinks sold there. Simple? Stratified? Systematic? Systematic; customers were chosen at a given interval (every 10th one).

10. T o determine the number of students who use computers to do their homework, the middle school office chooses 10 students at random from each grade and then interviews the students. Sample? 10 6th, 10 7th, and 10 8th grade students Population? All students in the school Biased? Unbiased? Why? Unbiased Simple? Stratified? Systematic? Stratified; students were chosen from similar, non-overlapping groups.

11. Popular Forms of Samples That Can Be Biased Convenience Convenient means EASY; a convenience sample will consist of members that are easily accessible. The HS administration wanted to evaluate how homecoming week was conducted at school. Every female member of the ASB class was asked how she liked the activities that week. It was convenient to sample the students in just one class. Voluntary Response A voluntary response sample will only include members who want to participate in the sampling. Paper surveys are sent home for the parents of 8th graders to ask their opinions about the homework policy. This is voluntary because only those who choose to do the survey will return it.

12. To find out more about the music preferences of their customers, the owners of a music store asked 20 customers who expressed interest to participate in an in-store interview. During the interview they listened to new CDs from artists in all music categories. Sample? 20 customers of the music store Population? All customers of the music store Convenience or Voluntary Response Sample? Voluntary Response; only the opinions of those customers who were interested in doing an interview about music preferences were sampled

13. During the April meeting, the president of the PTSA asked 6 parents and 6 teachers for their opinions on whether the 8th grade promotion dance should be held the week before promotion or the night after promotion. Sample? 6 parents and 6 teachers Population? All parents and teachers of the school Convenience or Voluntary Response Sample? Convenience; it was handy to ask their opinions since they were all in one place

14. Unbiased Samples biased Samples • Simple random • Systematic random • Stratified random • Convenience • Voluntary Response

15. Identify the Sample Sonia has been asked to determine whether the students at her school think there should be any “A” period classes next year. She asks 20 of her friends who are in her 7th grade “A” period math class. 17 of them said they thought there should be “A” period classes. Sonia reported that 85% of students polled supported the idea of having early classes next year. Sample? 20 students in Sonia’s “A” period math class Population? All students in the school Biased or Unbiased? Classify Biased sample—only those already taking a class were sampled Convenience Sample

16. Identify the Sample A shoe manufacturer wants to check the quality of the shoes produced by its employees. Every 15 minutes, five pairs of shoes are pulled off the assembly line to have a careful inspection for quality. Sample? 5 pairs of shoes, every 15 minutes Population? All shoes on the assembly line Biased or Unbiased? Classify Unbiased sample Systematic random sample

17. Practice Problems—Write Your Responses to the Questions 1. The owners of a mall want to know if they should put a movie theater in the mall. Every hour, the mall manager questions 20 of the people coming into the mall. What is the sample? What is the population? Is the sample simple, stratified, or systematic?

18. 2. A sub sandwich store owner wants to make sure that his employees are correctly weighing the meat that is put on the sandwiches. He watches an employee weigh the meat for one hour. Is the sample biased or unbiased? 3. A fast food restaurant is testing a new food item. To test if the customers are satisfied, the store owner asks the first 15 customers of the day if they would purchase the item. What is the sample? What is the population? Is it a convenience or a voluntary response sample?

19. 4. A state tourism board wants to determine the state’s favorite camping site. They send a survey to all mailing addresses in the state to be filled out and mailed back to them. What is the sample? What is the population? • Is the sample unbiased or biased? • If unbiased, classify it as simple, stratified, or systematic. • If biased, classify it as convenience or voluntary response.

20. Answers: • Sample: a group of shoppers at the mall, 20 every hour • Population: all mall shoppers • Systematic random sample: people are chosen according to a given time interval • Biased: he’s only watching one employee for one hour • Sample: first 15 customers of the day • Population: all the customers of the restaurant • Sample: people in the state with a mailing address • Population: all the people in the state • Biased: only residents will be surveyed • Voluntary response: only those who want will mail their response