10.4 Random Sampling

Jeanne pulled a marble out of a bag at random, recorded the color, and placed the marble back into the bag three times. The results are shown below.

• 2 blue • 1 red

She concluded that the bag contained exactly 4 blue marbles and 2 red marbles. To verify her conclusion, she then pulled an additional 15 marbles out of a bag using the same procedure. The results for all are shown below.

• 5 blue • 7 white • 6 red

Which best explains why Jeanne’s conclusion is incorrect?

• She drew a blue marble first.

• Her sample size was too small.

• She drew more red than blue marbles.

• Her method for selection should not have been random.

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Ryan wants to find the favorite video game of the fifth grade boys at his school. Which group would be best for Ryan to survey?

• 25 fifth grade boys

• 25 fifth grade students

• every teacher at his school

• every boy who will pass to fifth grade next year

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Ms. Jimerson asked students how much time they spent studying for their final exams. This dot plot shows the results.

Based on the dot plot, what is the approximate number of students that studied more than 2 hours if there are 450 students in the school?

• 225

• 158

• 135

• 64

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Scientists want to estimate the cheetah population in an area.

They tagged and released 29 cheetahs.

Later, they found 120 cheetahs, 9 of which were tagged.

Based on this information, what is the approximate cheetah population in this area?

• 129

• 158

• 387

• 1,080

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An amusement park employee was surveying people waiting in line to ride a roller coaster. Each person was asked whether waiting in line was worth their time. Which statement best explains why the significance of the survey results might be misinterpreted?

• People could be waiting in the wrong line.

• People could be waiting in line for a short period of time.

• People waiting in line have already shown a willingness to wait.

• People already waiting in line could simply be holding a place for friends.

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A beverage company prints game pieces on the inside of bottle caps and claims that one in six wins a prize. Catherine bought six bottles and did not win. Which statement is the best explanation for why she did not win?

• The company made an incorrect claim.

• Catherine bought all the bottles at the same time.

• Catherine did not buy them from different locations.

• The company made the claim based on a large quantity of bottles.

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Truck drivers in Miami were recently asked in a survey which type of car fuel they thought American drivers would be using in ten years. The results of this survey are shown in the table.

Which statement best describes why the results are biased?

• The sample size used is too small.

• The numbers are in descending order.

• The order of the fuel types is not alphabetical.

• The sample population is not representative of American drivers.

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Bert’s new high school plans to choose school colors by the end of the month. Bert surveyed 100 band students for their color preferences in the chart.

Which statement best describes why Bert’s data is misleading?

• The population sample is not identified by age.

• It does not give the percentage for each color combination.

• It does not identify the grade level of the students surveyed.

• The entire school population is not represented in the survey.

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A research group wants to know what types of car accessories drivers prefer. The research group will survey 1000 people. Which group would be BEST to use as a sample?

• employees at a car repair shop

• people who answered the phone

• drivers who stopped for gas at a service station

• high school students who just got their driver’s licenses

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Lee read a report on a survey showing that 80% of the adult population in one southern state, enjoy hot weather. In summarizing the report to her class, Lee stated that a majority of adults in the United States enjoy hot weather. What did Lee overlook in this statement?

• that only adults were included in the report

• that 80% is not a majority of the group surveyed

• that hot weather was not defined as a specific temperature range

• that conducting a similar survey in other parts of the country may produce different results

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