According to pg. 55 of Statistics in Plain English, the t-statistic for the sample mean is
$$ t = \frac{\bar{x} - \mu}{s} $$
where $\bar{X}$ is the sample mean, $\mu$ is the population mean, and $s$ is the sample estimate of the standard error.
Question: How is the sample estimate of the standard error computed in this context? In particular, does it make use of the population mean or the sample mean? That is, is it computed like this
$$ s = \sqrt{E[(S-\mu)^2]} $$
or
$$ s = \sqrt{E[(S-\bar{x})^2]}? $$
where $\bar{x}$ is the sample mean and $S$ is the sample from $X$ (the underlying random variable we are inspecting) viewed as a random variable.
When you go for t statistic, it is assume that you do not know the population standard deviation.
To answer your question, the sample standard deviation is calculated based on the below formula
$$s = \sqrt{\frac{\sum_{1}^{n}(x_i -\bar x)^2}{n-1}}$$