To estimate the number of participants in the soccer club that plan to play again next season, we can use the sample data to find the proportion of members who plan to play again.
In the sample:
- Number of members surveyed = 20
- Number of members who plan to play again = 14
First, we calculate the proportion of members from the sample who plan to play again:
\[ \text{Proportion} = \frac{\text{Number of members who plan to play}}{\text{Total number of members surveyed}} = \frac{14}{20} = 0.7 \]
This proportion indicates that 70% of the surveyed members plan to play again next season.
Now, we apply this proportion to the total number of members in the soccer club to estimate the total number of members who will play again:
\[ \text{Estimated number of members who will play again} = \text{Total members} \times \text{Proportion} \]
\[ \text{Estimated number} = 700 \times 0.7 = 490 \]
Thus, the estimated number of participants in the club that plan to play again next season is 490.