Lesson 14

Sampling in a Fair Way

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Problem 1

The meat department manager at a grocery store is worried some of the packages of ground beef labeled as having one pound of meat may be under-filled. He decides to take a sample of 5 packages from a shipment containing 100 packages of ground beef. The packages were numbered as they were put in the box, so each one has a different number between 1 and 100.

Describe how the manager can select a fair sample of 5 packages.

Solution

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Problem 2

Select all the reasons why random samples are preferred over other methods of getting a sample.

A:

If you select a random sample, you can determine how many people you want in the sample.

B:

A random sample is always the easiest way to select a sample from a population.

C:

A random sample is likely to give you a sample that is representative of the population.

D:

A random sample is a fair way to select a sample, because each person in the population has an equal chance of being selected.

E:

If you use a random sample, the sample mean will always be the same as the population mean.

Solution

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Problem 3

Jada is using a computer’s random number generator to produce 6 random whole numbers between 1 and 100 so she can use a random sample. The computer produces the numbers: 1, 2, 3, 4, 5, and 6. Should she use these numbers or have the computer generate a new set of random numbers? Explain your reasoning.

Solution

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Problem 4

A group of 100 people is divided into 5 groups with 20 people in each. One person’s name is chosen, and everyone in their group wins a prize. Noah simulates this situation by writing 100 different names on papers and putting them in a bag, then drawing one out. Kiran suggests there is a way to do it with fewer paper slips. Explain a method that would simulate this situation with fewer than 100 slips of paper.

Solution

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(From Unit 8, Lesson 6.)

Problem 5

Data collected from a survey of American teenagers aged 13 to 17 was used to estimate that 29% of teens believe in ghosts. This estimate was based on data from 510 American teenagers. What is the population that people carrying out the survey were interested in?

A:

All people in the United States.

B:

The 510 teens that were surveyed.

C:

All American teens who are between the ages of 13 and 17.

D:

The 29% of the teens surveyed who said they believe in ghosts.

Solution

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(From Unit 8, Lesson 12.)

Problem 6

A computer simulates flipping a coin 100 times, then counts the longest string of heads in a row.

Based on these results, estimate the probability that there will be at least 15 heads in a row.

trial most heads in a row
1 8
2 6
3 5
4 11
5 13

Solution

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(From Unit 8, Lesson 7.)