We appreciate your visit to A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie Among the 1500 respondents 13 chose chocolate. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
In this question, we are looking at a poll result about people's favorite pie, specifically chocolate pie. Out of 1500 adults surveyed, 13% of them said that chocolate pie was their favorite.
The key point here is understanding what the 'margin of error' represents in the context of this survey.
Margin of Error: It reflects the level of uncertainty in the survey results. In this case, it's plus or minus 33 percentage points. This means the calculated percentage (13%) could vary by up to 33 percentage points in either direction.
Interpreting the Margin: The margin gives a range for the true proportion in the population. Thus, the survey results suggest that the true percentage of all adults who might prefer chocolate pie could be as low as $13% - 33% = -20%[tex]or as high as $13\% + 33\% = 46\%[/tex]. Since a percentage can't be negative, the lower end would effectively be 0%, and the upper end 46%.
Confidence: Often, when a margin of error is stated, it involves a certain confidence level (such as 95%) that the true population proportion lies within the margin of error. However, this detail isn't provided here.
Considering the given choices:
A. The statement indicates that the study is 100% - 33% = 67% confident that the true population percentage of people that prefer chocolate pie is 13% is inaccurate because margin of error doesn't directly relate to a confidence percentage in this way.
B. The statement indicates that the interval 13% plus or minus 33% is likely to contain the true population percentage of people that prefer chocolate pie is the correct interpretation.
C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 13% plus or minus 33% is misleading as it doesn't mention probability or confidence.
D. The statement indicates that the study is only 33% confident that the true population percentage of people that prefer chocolate pie is exactly 13% is incorrect because the margin implies variability around 13%.
Therefore, the correct answer is B.
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