Lesson $$ 10-5 $$ Using Sampling to Predict (pp. 462-4 16. To determine the weekly top ten songs, the local radio station asks people to log on to their Web site and vote for their favorite song. Identify the sample as biased or unbiased and describe its type. Explain. 17. Forty-five out of 60 people at a steakhouse said their favorite meal was steak. Is this sampling representative of the entire town? If so, how many of the 13,000 residents would say steak was their favorite meal?

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**16. Analysis of the Sample for Weekly Top Ten Songs**

- The radio station collects votes by asking people to log on to their website.
- This means that only those who have Internet access and are motivated to vote will be included. This type of sampling is known as a **voluntary response sample**.
- Because individuals self-select into the sample, it is prone to **bias**. People with strong opinions (either for or against certain songs) are more likely to participate.
- **Conclusion:** The sample is biased and it is a self‐selected (voluntary response) sample.

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**17. Analysis of the Steakhouse Survey**

- In the survey, $$45$$ out of $$60$$ people at a steakhouse said their favorite meal was steak. The fraction of steak lovers in this sample is 
  $$
  \frac{45}{60} = 0.75.
  $$
- To assess representativeness:  
  The sample is taken only from a steakhouse, so those surveyed are more likely to be steak enthusiasts compared to the town’s overall population. Therefore, the sample may not be representative of the entire town.
- However, if we assume (for the sake of the exercise) that the sample is representative of the town's preferences, we can predict the number of residents who favor steak.
- For a town with $$13,\!000$$ residents, the estimated number of people whose favorite meal is steak would be:
  $$
  0.75 \times 13000 = 9750.
  $$
- **Conclusion:**  
  Although the survey is likely not representative because it only includes steakhouse patrons, if we assume it is representative, about $$9750$$ residents would say steak was their favorite meal.
**16. Sample Analysis for Weekly Top Ten Songs** - **Type of Sample:** Voluntary response sample. - **Bias:** Biased. - **Reason:** Only people with internet access and those who choose to vote are included, leading to potential bias. --- **17. Steakhouse Survey Analysis** - **Sample Size:** 60 people. - **Number Favoring Steak:** 45. - **Assumed Representation:** If the sample represents the entire town, approximately 9,750 out of 13,000 residents would prefer steak. - **Note:** The sample may not be representative since it only includes steakhouse patrons.

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