“As n increases, the absolute value of the tcritical falls, reducing the width of the confidence intervals.”
Why is this? Surely if n increases then the numerator in the following formula increases, which means that the tcritical increases:
t= [r (n-2)^1/2]/[(1-r^2)^1/2]
The only reason I can think of where this wouldn’t be the case, is if the correlation coefficient ® increases more than n as n increases or something. Any help here would be appreciated folks!
One way to look at this is sample "n "increases, the sample value approaches the population value hence we can say with more considence the value of X. If n increases to the extent that n matches the population, then the internals will be zero ie the larger the sample the smaller the confidence intervals.
Alternatively you can look at the formula below:
Population value = Sample value +/- t x SE
P = b +/- tx SE
As n increases SE reduces and hence the value of P will have lower considence intervals.