Question

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.

No, 0.10(8,000,000) = 800,000, which is more than the sample.
No, 10(8,000,000) = 80,000,000, which is more than the sample.
Yes, 0.10(3,000) = 300 students, which is less than the total population.
Yes, 10(3,000) = 30,000, which is less than the total population.
There is not enough information to determine whether the 10% condition is met.

Answer 1

Therefore the correct option is D.) Yes, 10(3000) = 30,000 which is less than the population.

Explanation:

i) Sample size = 3000

ii) the condition for a sample is that the sample size cannot be over 10% of population

iii) population size is = 8,000,000 (8 million)

iv) therefore 10% of 8,000,000 = 800000 which is more than 3,000

So the answer is Yes. the 10% condition is met.

Therefore the correct option is D.) Yes, 10(3000) = 30,000 which is less than the population.