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Chapter 7: Problem 104

You want to find the mean weight of the students at your college. You calculate the mean weight of a sample of members of the football team. Is this method biased? If so, would the mean of the sample be larger or smaller than the true population mean for the whole school? Explain.

Short Answer

Expert verified
Yes, the method is biased as it samples only football team members who might not accurately represent the entire student population in terms of weight. The sample mean is likely to be larger than the true mean, as athletes usually tend to weigh more.

Step by step solution

01

Identify the bias in the sampling method

Bias in a sampling method refers to a systematic discrepancy between the characteristics of the sampled group and those of the entire target population. In this scenario, sampling students from the football team introduces bias as these students might not be an accurate representation of the entire student body in terms of factors like physical fitness, diet, and body size, which influence the weight of an individual.
02

Recognize the direction of the bias

After identifying the bias in the sampling method, it's important to determine the direction of the bias -- does it result in overestimation or underestimation of the population characteristic (mean weight)? In this case, given that athletes generally have more lean mass and potentially a larger build due to training, it is likely that the mean weight of the football team would be higher than the mean weight of the general student population. Therefore, the bias would result in an overestimation of the population mean weight.
03

Explain the Conclusion

As reasoned in Step 2, the bias in the sampling method (sampling only from the football team) is likely to result in an overestimation of the population mean weight. The discrepancy happens due to the bias in sampling, emphasizing the importance of selecting a representative sample when estimating population characteristics.

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Most popular questions from this chapter

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