Calculating standard deviation after increasing sample size ?? 10 points BA?

Question

A poll of 93 students found that 35% were in favor of raising tution to build a new math building. The standard deviation of this poll is 6%. What would be the standard deviation if the sample size were increased from 93 to 267?

Leonard · Accepted Answer

I dont agree that the std dev of the poll is 6%. The std dev of a percentage is sqrt(p (1-p)/n) =
sqrt((.35)(.65)/93) = .049, or 4.9%.

For a sample size of 267 (assuming the same 35% results), would be sqrt((.35)(.65)/267)=.029,
or 2.9%

Ẩn danh · Answer

If the sample is a perfect representation of your pool, then technically s.d. Shouldn't change...but this is rarely the case and randomness in the sample is what will affect s.d. When you change your sample by increasing or decreasing it. Hope this helps somewhat.

Calculating standard deviation after increasing sample size ?? 10 points BA?

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