A polling organization took a random sample of 3,000 middle school students to determine how many have a dog. Suppose that 57% of all middle school students have a dog. If the total population of middle school students is 8 million, is the 10% condition met? Justify your answer.

A. No, 0.10 (8,000,000) = 800,000, which is more than the sample.

B. No, 10 (8,000,000) = 80,000,000, which is more than the sample.

C. Yes, 0.10 (3,000) = 300 students, which is less than the total population.

D. Yes, 10 (3,000) = 30,000, which is less than the total population.

E. There is not enough information to determine whether the 10% condition is met.

Question

Mathematics

Phoenix

24 December, 01:14

A polling organization took a random sample of 3,000 middle school students to determine how many have a dog. Suppose that 57% of all middle school students have a dog. If the total population of middle school students is 8 million, is the 10% condition met? Justify your answer.

A. No, 0.10 (8,000,000) = 800,000, which is more than the sample.

B. No, 10 (8,000,000) = 80,000,000, which is more than the sample.

C. Yes, 0.10 (3,000) = 300 students, which is less than the total population.

D. Yes, 10 (3,000) = 30,000, which is less than the total population.

E. There is not enough information to determine whether the 10% condition is met.

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Answers (1)

Know the Answer?

Rhett Stein · Answer 1

D. Yes, 10 (3,000) = 30,000, which is less than the total population.

Step-by-step explanation:

The 10% condition means that the sample should not be more than 10% of the population. Or, put another way, 10 times the sample should be less than the population.

The sample is 3,000. 10 times the sample is 30,000. This is less than the population of 8 million. So the 10% condition is met.