Vocabulary population sample random sample convenience sample biased sample
In 2002, there were claims that Chronic Wasting Disease (CWD), or Mad Elk Disease, was spreading westward across North America. In order to verify claims such as these, the elk population had to be tested. When information is gathered about a group, such as the elk in North America, the entire group is called the population. Because testing each member of a large group can be difficult or impossible, researchers often study a part of the population, called a sample.
For a random sample, members of the population are chosen at random. This gives every member of the population an equal chance of being chosen. A convenience sample is based on members of the population that are readily available, such as 30 elk in a wildlife preservation area. A random sample is more likely to be representative of a population than a convenience sample is. Helpful Hint
Biased sampling: A sample drawn in such a way that one or more parts of the population are favored over others. Unbiased Sampling: A sample representative of the entire population.
Determine which sampling method will better represent the entire population. Justify your answer. Additional Example 1: Analyzing Sampling Methods Sampling method Maria surveys only the band students she knows personally. Results 84% want blue uniforms Jon writes each band student’s name on a card. He questions those students whose name he draws. 61% want blue uniforms Jon’s sample is a random sample, giving every band member equal chance to be surveyed, so it is the better method.
Determine which sampling method will better represent the entire population. Justify your answer. Check It Out: Example 1 Sampling method Ferdinand surveys every other swimmer on the team. Results 72% want practice early Anna-Maria questions the swimmers who are in her Biology class. 50% want practice early Ferdinand’s sample is a random sample, giving results that better represent the entire swimming team, so it is the better method.
A biased sample does not fairly represent the population. A study of 50 elk belonging to a breeder could be biased because the breeder’s elk might be less likely to have Mad Elk Disease than elk in the wild.
Determine whether each sample may be biased. Explain. Example: Identifying Potentially Biased Samples A. The mayor surveys 100 supporters at a rally about the most important issues to be addressed by the city council. The sample is biased. The supporters may have different ideas than those not at the rally. B. The principal sends out questionnaires to all of the students to find out what kind of music students prefer at dances. The sample is random. The students all have a chance to respond.
A principal of a school with 1,500 students estimates that about 400 students will attend a band festival on Saturday. A random sample of 25 students showed that 6 of them will attend. Determine whether the principal’s estimate is likely to be accurate. Example: Verifying Claims Based on Statistical Data Set up a proportion to predict the total number of students that will attend. Students attending sample # of Students sampled Students attending Student Population =
Additional Example 3 Continued Let x represent the number of actual students attending the band festival. 6 25 x 1500 = 6 1500 = 25 xThe cross products are equal. 9000 = 25x Multiply. 9000 25 25x 25 = Divide each side by 25 to isolate x. 360 = x The estimate is not accurate because the data shows that 360 students are likely to attend.
a. A TV ratings service is surveying residents of Orlando who bought TVs in the last month about their favorite TV show. b. A TV ratings service called residents of Orlando randomly selected from the phone directory to conduct a survey about their favorite show. Lesson Quiz: Part I b 1. Determine which sample better represents the entire population.
2. Determine whether each sample may be biased. Explain. Lesson Quiz: Part II Biased; at other times of the day, customers may have different preferences. a. A convenience store surveys customers one morning to determine what products they may like the store to stock. b. Each student’s name is written on a slip of paper and placed in a box. One slip of paper is selected to determine the student to be the homeroom representative. Not biased; the sample is random.
3. A local middle school has 2500 students. Morgan interviewed 75 of the students about their library habits. She found that 45 of the students checked out a book weekly. Predict the number of students likely to check out books weekly. Lesson Quiz: Part III 1500