A sample of 30 high school students was selected at random and asked how much time they spent on social media each day. Of the high school students selected, 22
spend more than 1 hour on social media each day.
If the conclusion was drawn that "approximately 5.8 million high school students spend more than 1 hour on social media each day," which of the following is closest to the population, in millions, of high school students?
Approximately 22 out of 30 students or \(\dfrac{22}{30}\) of students spend more than 1 hour on social media. We can use a proportion:
$$ \frac{22}{30}=\frac{5.8}{\text{all students}} $$
$$\frac{22}{30}\cdot \text{all students}=5.8 $$
$$ \text{all students} = 5.8 \cdot \frac{30}{22} $$
$$ \approx \boxed{7.91} $$
If 22 out of 30 students are representative of the entire population, that means more than half (15) of all high school students use social media for more than 1 hour each day.
Since we know that 5.8 million is more than half of all students, only \(\boxed{7.91}\) is reasonable. The entire population cannot be less than 5.8 million, which rules out the first two options. 5.8 is less than half of 13.71, so it doesn't fit the initial condition.