I'm reading Experimental Design and Data Analysis for Biologists by Professor Quinn and Profesoor Keough and, on page 20, they write -
We can use the methods just described to reliably determine standard errors for statistics (and confidence intervals for the associated parameters) from a range of analyses that assume normality, e.g. regression coefficients. These statistics, when divided by their standard error, follow a t distri- bution and, as such, confidence intervals can be determined for these statistics (confidence interval = t * standard error).
What I understand is two things:
a) Our sample statistics follows is normally distributed, because of the central limit theorem, but we need to use the t-distribution because we don't know the standard deviation of the parameter.
b) We use the t-distribution to calculate the confidence interval so that we capture 95%, or some percent, of the possible values for the parameter.
I have two questions: Is that accurate and, why do we divide our statistic by the standard error? Why not just use the distribution of the sample statistic?