Question

In a sample of people at the school dance 11 out of 15 were in favor of having the photo booth. If all 300 students were surveyed about the photo booth how many are likely to be in favor of the photo booth?

Answer 1

Answer:

If all the 300 students were surveyed, 220 would have been in favor of the photo booth.

Step-by-step explanation:

Sample size = 15

People out of 15 in favor of photo booth = 11

Percentage of people in favor of school dance = $\frac{11}{15} \times 100\% = 73\frac{1}{3} \%$

We have to find if all 300 students are surveyed how many will be in favor of photo booth. Remember that, the sample data is the best estimator of the population data. So, the sample data of 15 students will be the best estimator for the entire population of 300 students.

Since, in the sample of 15 students, $73\frac{1}{3} \%$ were in favor of photo booth, we would expect that if all the 300 students were surveyed, the same percentage will be in favor of photo booth. So we need to calculate $73\frac{1}{3} \%$ of 300.

$73\frac{1}{3} \% \text{ of 300}\\\\ = 73\frac{1}{3} \% \times 300\\\\ =\frac{220}{3} \% \times 300\\\\ =\frac{220}{300} \times 300\\\\ = 220$

This means if all the 300 students were surveyed, 220 would have been in favor of the photo booth as per the sample data.