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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The sample in question is biased. Since the local radio station only solicits votes from people visiting their website, it likely attracts a specific audience who are already interested in the station's music or the particular songs being played. This skewing means that the sample is not representative of the general population's musical preferences, as it excludes those who may not use the website or engage with the station—such as casual listeners or individuals who prefer different genres. As for the steakhouse situation, while the survey suggests that a significant portion of those surveyed prefer steak, it might not be representative of the entire town. If we take the sampling at face value (45 out of 60), that gives a rough rate of 75%. To extrapolate this to the town's population (13,000 residents), we find that 75% of 13,000 is about 9,750. However, caution is important—this calculation assumes the surveyed group reflects the broader community's preferences accurately, which might not be the case given the location and nature of the survey.