How do I find the minimum sample mean needed to estimate a population mean to within 2.5cm with 99%confidence?
I can not figure out how to do this, can someone PLEASE help! :)
Question: The typical mean volume of the white matter in the cerebrum of a 2 year old is 250cm3 with a standard deviation of 4.5cm3.
What would be the minimum sample needed to estimate the population mean volume of cerebellum white matter to within 2.5cm with 99% confidence?
- 9 years agoFavorite Answer
So here is the information we have:
x bar: 250
We would first use the 99% confidence level to find z*; We could use a calculator and do -invnorm((1-.99)/2), which is located under the Distributions menu, or use a table. I happen to have my calculator handy, so I used it and got a z* value of 2.576.
Margin of error (which is given as 2.5cm) is defined as z* multiplied by std.deviation/√n.
Thus, we can set up the equation 2.5=2.576(4.5/√n).
Now it's just a matter of simple algebra!
Divide both sides by 2.576, and you will get:
Now just cross multiply and isolate n on its own side of the equation
Square both sides, and you get 21.522, but since there is no way we can take a sample of a half-person, and truncating would cause us to miss our target for the margin of error, we would round up, and say that our minimum sample size is 22.
Hope this helps! :-)