Understand Representative Samples LESSON 12.1 More Practi Homework For Problems 1-3, use the following information. The president of a national soccer fan club, Abdul, wants to determine if the club's 10,000 members are in favor of using club dues to make a new online video to support their team in the upcoming championship. He assigns a number to each member and uses a random number generator to choose 250 members to survey. 1. Identify the population and sample. $$ \qquad $$ Papulation: All 10,000 members sample 2. Is the sample representative of the entire population? Explain. $$ \qquad $$ $$ \qquad $$ 3. Suppose 212 of the 250 members in a random sample are in favor of using club dues to make a new video for their team. What can Abdul conclude about the results of the survey? Explain. $$ \qquad $$ $$ \qquad $$

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1. **Population and Sample**

- Population: All $$10,\!000$$ members of the fan club.
   - Sample: The $$250$$ members selected via a random number generator.

2. **Representativeness of the Sample**

A sample is considered representative if it is drawn in such a way that every member of the population has an equal chance of being selected. Since the $$250$$ members were chosen randomly using a random number generator, this method helps ensure that the sample is not biased. Thus, the sample is likely representative of the entire population.

3. **Interpreting the Survey Results**

In the survey, $$212$$ out of $$250$$ members are in favor of using club dues to make a new video. This gives a sample proportion of in favor as
   $$
   \hat{p} = \frac{212}{250} \approx 0.848.
   $$
   This result suggests that approximately $$84.8\%$$ of the surveyed members support the initiative. Based on this random sample, Abdul can reasonably conclude that there is strong support among the club members for using dues to create a new video. However, while the sample is likely representative, he should consider the margin of error and possibly construct a confidence interval before making a final decision.
1. **Population and Sample** - **Population:** All 10,000 members of the fan club. - **Sample:** 250 members selected randomly. 2. **Representativeness** The sample is likely representative because it was chosen randomly, giving every member an equal chance of being selected. 3. **Survey Results** 212 out of 250 members support using club dues for a new video, which means about 84.8% of the surveyed members are in favor. Abdul can conclude that there is strong support among the club members for this initiative.

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