Question

Would this one be worked out like the last. I dont know what the mean would be.
A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 95% confident that her estimate is correct. If the standard deviation is 5.35, how large a sample is needed to get the desired information to be accurate within 0.64 decibels? Show all work.

Answer 1

. She wants to be 95% confident that her estimate is correct. The estimate of the mean should be with ± 2\(\sigma\)
accurate within ± 0.64 decibels equates with ± 2σ
so the sigma she needs is σ = 0.64/2 = 0.32 decibels

The standard deviation of the data she is measuring is \(σ_D\)= 5.35
if she uses N samples to estimate the mean, the uncertainty σ of her estimate of the mean will be \[ \frac{σ_D}{\sqrt{N}} = 0.32\]
solve for N