Presentation on theme: "Populations and Samples"— Presentation transcript:
1Populations and Samples Notes 54Populations and Samples
2Vocabulary Population- the entire group. Sample- part of the population that is studied.Random sample- members of the population are chosen at random.Convenience sample- based on members of the population that are readily available.Biased sample- does not fairly represent the population.
3For a random sample, members of the population are chosen at random 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
4Additional Example 1: Analyzing Sampling Methods Determine which sampling method will better represent the entire population. Justify your answer.61% want blue uniformsJon writes each band student’s name on a card. He questions those students whose name he draws.Results84% want blue uniformsSampling methodMaria surveys only the band students she knows personally.Jon’s sample is a random sample, giving every band member equal chance to be surveyed, so it is the better method.
5Check It Out: Example 1Determine which sampling method will better represent the entire population. Justify your answer.65% said the quarterback wasthe most valuable player.Chad puts all of his team members’ names in a hat and draws the names of 10 players at random. He then asks each of those players to name the team’s most valuable player.Results87% said the quarterback was the most valuable player.Sampling methodPedro asks each member of thefootball team’s offense to name the team’s most valuable player.
6A biased sample does not fairly represent the population 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.
7Additional Example 2: Identifying Potentially Biased Samples Determine whether each sample may be biased. Explain.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 chooses student names at random and asks them what kind of music they prefer at dances.The sample is not biased. It is random because every student has a chance to respond.
8Check It Out: Example 2Determine whether the sample may be biased. Explain.The owner of a record shop surveys only customers over the age of 18 who shopat his store.
9Additional Example 3: Verifying Claims Based on Statistical Data A principal of a school with 1,500 students estimates that about 350 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.Set up a proportion to predict the total number of students that will attend.Students attending sample # of Students sampledStudents attending Student Population=
10Additional Example 3 Continued 6 25xLet x represent the number of actual students attending the band festival.=6 • 1500 = 25 • xThe cross products are equal.9000 = 25xMultiply.25x 25=Divide each side by 25 to isolate x.360 = xBased on the sample, you can predict that 360 students will attend the band festival. The principal’s estimate is likely to be accurate.
11Check It Out: Example 3The owner of a large chain restaurant with 1,200 employees estimates that about 250 employees will ask for winter vacation. A random sample of 40 employees showed that 8 of them will ask for the time off. Determine whether the owner’s estimate is likely to be accurate.