Minimum sample size

#1
Hi Everyone,

I have spent hours on this and cannot seem to get to the answer.

Here is the questions:

Calculate the minimum number of children that will be needed in the study to allow paired and unpaired analysis to be performed based on the the following assumptions. First, it is assumed that the within child standard deviation of hearing is 14.25 decibels, and secondly, that the between child ST Dev of hearing is 11.4 decibels. Finally it is thought that 10 decibels should be the minimum differecne in levels of hearing between treatments that be regarded as clinically important and that the trials have a 95% chance of detecting such a difference between the two treatments at the two sided 5% level of significance.

I thought that N= 7.8 or 8 rounded for paired based on N = 1.96^2 X 14.25^2/10^2 but this does not seem right and what would you use for the unpaired analysis?

Please help I have looked at loads of different formulas.