Stat 100

[BarTopDancer]

Halp - Margin of Error

Question:

A question on a youth survey was “How well do you get along with your parents?” The survey showed that 54% of the randomly selected teenagers said they get along “very well.” The reported margin of error was 5%. Is it reasonable to infer that the majority of teenagers get along “very well” with their parents? Provide reasoning.

My Answer:

According to the table in the syllabus, a 5% margin of error would mean 400 teens were surveyed. A 5% margin of error also brings down the sample percent to 49% of teens that say they get along very well with their parents. This means the majority of teens do not say they get along “very well” with their parents. However, if a larger sample was used and the margin of error shrank it is highly probable that the percentage would show that the majority of teens say they do get along very well with their parents.

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Am I on the right track or over-thinking it again?