Preview Warm Up California Standards Lesson Presentation

Warm Up Solve. 1. What percent of 25 is 8? 2. 16 is what percent of 80? Find the mean of each data set. 3. 11, 12, 9, 10, 16, 14 4. 65, 70, 15, 98, 88, 16, 62, 38 Solve each proportion. 5. = 6. = 32% 20% 12 56.5 4 15 t x t 75 65 300 t n t 60 20 13

California Standards SDAP2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample. Also covered: NS1.3, SDAP2.5

Vocabulary population sample random sample

In 2002, there were claims that Chronic Wasting Disease (CWD), or Mad Elk Disease, was spreading westward across North America. In order to evaluate these claims, the elk population had to be tested. A population is an entire group of objects or individuals that is considered for a survey. All of the elk in North America is an example of a population. Surveying or testing every member of a large group can be difficult or impossible. Instead, researchers often study a sample. A sample is a part of the population.

In a random sample, each member of the population has an equal chance of being selected. A random sample is more likely to be representative of a population than samples that are chosen in other ways.

Additional Example 1: Deciding When to Use a Sample For each situation, explain whether it makes sense to use a sample. A. The manager of a store wants to know the average age of the store’s customers. The entire population is large. It would be difficult to find out the age of every customer. It does make sense to use a sample. B. The manager of a store wants to know the average salary of the store’s 8 employees. The entire population is small. It does not make sense to use a sample because every employee can be evaluated.

Additional Example 2: Comparing Samples About 39% of all U.S. households have houseplants. Lee surveys a random sample of households from two towns in his state. Compare the samples with the national percent. Houseplant Ownership Sample With Plants Without Plants Town A 40 60 Town B For each sample, find the percent of the households that have houseplants.

Additional Example 2 Continued About 39% of all U.S. households have houseplants. Lee surveys a random sample of households from two towns in his state. Compare the samples with the national percent. Town A: = = # of households with plants total number of households t 40 t 40 + 60 t40t 100 = 0.40 = 40% Town B: = = # of households with plants total number of households t 60 t 60 + 40 t60t 100 = 0.60 = 60% The percent of households with houseplants in Town A (40%) is close to the national percent. The percent of households in Town B (60%) is greater than the national percent.

Additional Example 3: Evaluating Claims Based on Statistical Data A Web site consists of 400 pages. A Web designer estimates that 60 of the Web pages have broken links. In a random sample of 20 pages, 7 of the pages have broken links. Determine whether the manager’s estimate is likely to be accurate. Explain. Set up a proportion to predict the total number of broken links. broken links in sample pages sampled total # of broken links # of web site pages =

Additional Example 3 Continued 7 20 x 400 Let x represent the number of actual links broken. = 7 • 400 = 20 • x The cross products are equal. 2800 = 20x Multiply. 2800 20 20x 20 = Divide each side by 20. 140 = x The estimate is not accurate because based on the sample, the number of pages with broken links is likely to be about 140.

Check It Out! Example 1 For each situation, explain whether it makes sense to use a sample. A. A veterinarian wants to know the average number of pets in her town. The entire population is large. It would be difficult to find out the number of pets in a town. It does make sense to use a sample. B. The veterinarian wants to determine how many pets she can house in her 10 kennels. The entire population is small. It does not make sense to use a sample because every kennel can be evaluated.

Check It Out! Example 2 About 22% of all U.S. households have pet fish. Rylan surveys a random sample of households from two towns in his state. Compare the samples with the national percent. Pet Fish Ownership Sample With Pet Fish Without Pet Fish Town A 25 75 Town B 55 45 For each sample, find the percent of the households that have pet fish.

Check It Out! Example 2 Continued About 22% of all U.S. households have pet fish. Rylan surveys a random sample of households from two towns in his state. Compare the samples with the national percent. Town A: = = # of households with pet fish total number of households t 25 t 25 + 75 t25t 100 = 0.25 = 25% Town B: = = # of households with pet fish total number of households t 55 t 55 + 45 t55t 100 = 0.55 = 55% The percent of households with pet fish in Town A (25%) is close to the national percent. The percent of households in Town B (55%) is greater than the national percent.

Check It Out! Example 3 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. Explain. Set up a proportion to predict the total number of students that will attend. Employees surveyed for time off # of Employees surveyed Employees asking for time off Total # of Employees =

Check It Out! Example 3 Continued 8 40 x 1200 = Let x represent the number of actual employees asking for time off. 8 • 1200 = 40 • x The cross products are equal. 9600 = 40x Multiply. 9600 40 40x 40 = Divide each side by 40. 240 = x The estimate is accurate because the data shows that 240 employees are likely to ask for time off.

No; the population is small. Lesson Quiz: Part I 1. Explain whether it makes sense to use a sample if you want to know the average length of dolphins at the aquarium. No; the population is small.

Beach Visits in the Past Year Lesson Quiz: Part ll 2. About 22% of Americans go to the beach each year. Amanda surveys a random sample of people from two towns. Compare the samples with the national percent. Beach Visits in the Past Year Sample Yes No Town A 56 24 Town B 16 64 The percent of people from Town A who visited the beach (70%) is greater than the national percent. The percent of people from Town B (20%) is close to the national percent.

Lesson Quiz: Part IIl 3. A doctor has 600 patients. She estimates that 175 of them exercise nearly every day. She surveys a random sample of 40 patients and finds that 12 exercise nearly every day. Determine whether the doctor’s estimate is likely to be accurate. Explain. Yes; based on the sample, you can predict that 180 patients exercise nearly every day.