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A commercial once noted that 4 out of 5, or 80%, of dentists recommend their product for dental health. Skeptical of the claim, Breanna took a random sample of 120 dentists in her state and noted that 70% of the dentists would recommend the product to improve dental health. She then used 70% as an estimate of the true proportion of dentists that would recommend the product and simulated 100 samples of size 120. What is the estimate of the margin of error for Breanna’s estimate of the proportion of dentists who would recommend the product?

a) 10%
b) 15%
c) 5%
d) 7.5%

User Tony Wang
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1 Answer

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Final answer:

The margin of error for Breanna’s estimate without any additional information is inferred from the multiple-choice options to be 10%, corresponding to the difference between her sample proportion and the claimed proportion.

Step-by-step explanation:

To estimate the margin of error for Breanna’s estimate of the proportion of dentists who would recommend the product, we consider the sampling distribution of the proportion with the simulated samples. A common approach to finding the margin of error is to use the formula for the margin of error of a proportion, which is ME = z * sqrt[(p(1-p)/n)], where ME is the margin of error, z is the z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.

In this case, since the confidence level is not provided, we are unable to calculate the exact margin of error without additional information. However, as this is a multiple-choice question, we can derive that the margin of error would be the difference between the sample proportion (70%) and the assumed true proportion according to the claim (80%), resulting in a 10% difference. Therefore, the closest answer choice provided that represents this difference is (a) 10%.

It's important to note that the margin of error really should be calculated using the appropriate z-score for the desired confidence level and the sample data. In practice, additional context from the simulation would be needed to determine the true margin of error.

User Adam Azad
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