Estimating a Population

Estimating a Sample A newspaper reporter arrives late to a game and sees a few remaining fans. The reporter knows nothing about the teams or the game but concludes that the home team lost. Describe how the reporter may have come to this conclusion.

Focus Question When can you use a small group to estimate things about a larger group?

Estimating a Population Find the constant of proportionality. Write an equation: (Estimated Number of items in population) = Target Items in Sample Total Items in Sample _____________ x Population Size

NUMBER OF ORANGE GOLF BALLS Estimating a Population NUMBER OF ORANGE GOLF BALLS The number of orange golf balls in the population is proportional to the number of orange golf balls in the representative sample.

# of orange sample size ___________ 2 6 __ 1 3 = (1/3)*150 = Approximately 50 orange golf balls in the bucket.

NUMBER OF GREEN GOLF BALLS Estimating a Population NUMBER OF GREEN GOLF BALLS The number of green golf balls in the population is proportional to the number of green golf balls in the representative sample.

# of green sample size ___________ 4 6 __ 2 3 = (2/3)*150 = Approximately 100 orange golf balls in the bucket.

Estimating a Sample 2 out of 10 are robots. Suppose it is 200 years in the future. The population consists of humans and robots. You collect a representative sample. If the population has 13,500 members, estimate the number of robots in the population. 2 out of 10 are robots. So our Constant of Proportionality is 1/5. 1/5 * 13,500 = Approx. 2,700 robots.

Estimating a Population In a representative sample of 24 seventh graders, there are 3 students with April birthdays. Suppose there are 448 students in the seventh grade. Estimate how many students in the seventh grade have April birthdays. 3/24 = 1/8 1/8 ·448=56

Estimating a Population How do you know that there is a constant of proportionality between a representative sample and the population? The traits in a representative sample MUST be proportional to the traits in the population. Otherwise it is not a representative sample.

Estimating a Population A botanist wants to find the number of four-leaf clovers in a field. There are 700 clovers in the field. She has three samples of the population. If the actual number of four-leaf clovers in the field is 6, which sample best represents the population? Sample 1 Sample 2 Sample 3 3, 3, 3, 4, 3 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4

Estimating a Population Sample A 1/5 * 700 = 140 Sample B 1/25 * 700 = 28 Sample C 1/100 * 700 = 7 The actual number of four-leaf clovers in the field is 6. Of Samples A, B, and C, Sample C is closest to the actual number. So Sample C best represents the population.

Estimating a Population You want to find the number of fiction books in your local library. There are 5,000 books in the library. You have three samples. The actual number of fiction books in the library is 1,500. Which sample(s) best represent the population? SAMPLE A: 2 fiction, children’s, biography, non-fiction, poetry, play SAMPLE B: 12 fiction, 15 non-fiction, and 12 biography SAMPLE C: 40 fiction, 29 non-fiction, 7 poetry, 19 drama, 39 children’s

Estimating a Population How is the estimate of a population affected by the size of the sample? The larger the sample size, the more accurate the estimate of the population.

Estimating a Population A computer factory has 670 computers in storage. Three inspectors each checked 50 of the computers in different areas of the storage room and noted the number of defective computers they found. Each inspector used his or her results to estimate the total number of defective computers in the factory.

Estimating a Population If each inspector checked 50 computers, what was each inspector’s estimate? A: B: C:

Estimating a Population Suppose the actual number of defective computers in storage is 29. Which inspector’s estimate is best? Explain.

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