Question

A soccer club has 700 members. A sample survey is taken, and 14 of the 20 members surveyed plan to play again next season. If this sample is representative of the soccer club population, estimate the number of participants in the club that play in the next season.

Answer 1

To estimate the number of participants in the club that plan to play next season, we can use the proportion of the surveyed members who plan to play and apply that proportion to the total membership of the club.

From the survey:
- Number of surveyed members = 20
- Number of those who plan to play again next season = 14

First, we calculate the proportion of surveyed members who plan to play again:

\[
\text{Proportion who plan to play} = \frac{\text{Number who plan to play}}{\text{Total surveyed}} = \frac{14}{20} = 0.7
\]

Next, we apply this proportion to the total membership of the soccer club:

\[
\text{Estimated number of members who plan to play} = \text{Total members} \times \text{Proportion who plan to play}
\]
\[
= 700 \times 0.7 = 490
\]

Thus, we estimate that **490 members** of the soccer club plan to play next season.