Math CC7/8 – Mar. 23 Math Notebook: Things Needed Today (TNT): Pencil/Math Notebook/calculator Sample & Population 2.1 Math Notebook: Topic: Comparing & Analyzing Sampling Method HW: Worksheet

What’s Happening Today? Lesson 2.1 –Sampling Methods Begin HW?

Warm Up 1) Which language has the fewest native speakers? Spanish 2) About how many more people speak Mandarin than Hindi? Approx: 500 millions

Comparing & Analyzing Sampling Methods 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.

Comparing & Analyzing Sampling Methods 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.

Depending on how the sample is selected, it may be possible to use the data to make predictions or draw conclusions about an entire population. The challenge is to choose a sample that accurately represents the population as a whole!

A strategy from choosing a sample from a population. Sampling Plan A strategy from choosing a sample from a population.

Comparing & Analyzing Sampling Methods Population Sample Helpful Hint A random sample is more likely to be representative of a population than a convenience sample is

Bias & Unbiased Biased or Unbiased. In survey sampling, bias refers to the tendency of a sample statistic to systematically over- or under-estimate a population parameter Bias often occurs when the sample does not accurately represent the population sampling bias is a bias in which a sample is collected in such a way that some members of the intended population are less likely to be included than others.

Biased or Unbiased Biased People attending a football game were asked what their favorite sport was. Orchestra students were asked if more money should be spent on the athletics programs. All 1st period students were asked where they want to go to college. People standing in line to see the latest Twilight series movie were asked what their favorite type of movie was. Biased Biased Unbiased Biased

Representative Sample A representative sample is a small quantity of something that accurately reflects the larger entity (group as a whole.) Example: is when a small number of people accurately reflect the members of an entire population A representative sample should be an unbiased indication of what the population is like.

Which of these is a good representative sample? Explain.

Which of these is a good representative sample? Explain.

How can we verify claims? 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.

Determine whether the owner’s estimate is likely to be accurate. The 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.

Thinking about surveys and samples... Why use a sample? Why might it be hard to get a truly random sample of a large population?

What is the population for the Honesty Survey? Suppose a national magazine asks its readers to respond to the questions below about honesty. Readers take the survey on the magazine’s Web site. What would you do if you found someone’s wallet on the street? Try to return it to the owner Return it, but keep the money Keep the wallet and the money What is the population for the Honesty Survey? Is asking readers to volunteer their answers a good way for the magazine to draw conclusions about the honesty of the population? Why or why not? 2. What would you do if a cashier mistakenly gave you $10 extra in change? Tell the cashier about the error Say nothing and keep the cash 4. Would you download music from the Internet illegally instead of buying the music? Yes b. No 3. Would you cheat on an exam if you were sure you wouldn’t get caught? Yes b. No 5. Do you feel that you are an honest person in most situations? Yes b. No

What is the population for the Honesty Survey? Note: Sampling Plan is a strategy for choosing a sample from a population. What is the population for the Honesty Survey? What is the sample? How was the sample chosen from the population? The population is the population of the United States. The sample is the readers of this particular magazine who log on and respond to the internet survey. The sampling plan is to ask people to answer the survey.

Suppose 5,280 people completed the survey. For the first question: 3,960 people said they would try to return the wallet to the owner; 792 said they would return the wallet but keep the money; and 528 said they would keep the wallet and the money. What is the relative frequency of each response? (3960/5280)(100) = 75% (792/5280)(100) = 15% (528/5280)(100) = 10% For the 2nd question: 4,752 people said they would tell the cashier about the error. What is the relative frequency of respondents who said they would tell the cashier about the error? 90% (4752/5280)(100) =

Suppose 5,280 people completed the survey. For the third question: 4,224 people answered “No.” What is the relative frequency of respondents said they would not cheat on an exam? (4,224/5280)(100) = 80% For the 4th question: 1,584 people answered “Yes.” What is the relative frequency of respondents that said they would not download music illegally from the Internet? 3, 696 5, 280 – 1, 584 = (3,696 / 70% 5,280)(100) =

Look & Analyze the table or graph that shows the relative frequencies of “honest” and “dishonest” answers for each of the first four questions of the Honesty Survey. .What conclusion can you draw about people’s behavior?

People are honest 70%-90% of the time. It appears that the more personal the interaction, the more likely the person is to act honestly.