Question

10.34 Explain why $s_p$ is called the pooled sample standard deviation.

Short answer

Let, $s_p$aggregates data from both samples' variability into a single estimate of the population standard deviation's common value. As a result, pooled standard deviation is referred to as $s_p$.

Step-by-step solution

Given information

To explain why $s_p$ is called the pooled sample standard deviation.

Explanation

A test statistic is used when running a hypothesis test based on independent samples to compare the means of two populations with equal and unknown standard deviations.
Individual sample variances of two populations, ${s_1}^2$and ${s_2}^2$, are taken and pooled by weighting them according to their sample size or degree of freedom, $n_1$and $n_2$, respectively.
$s_p=\sqrt{\frac{\left(n_1-1\right)s_1{}^2+\left(n_2-1\right){s_2}^2}{n_1+n_2-2}}$
Let, $s_p$ aggregates data from both samples' variability into a single estimate of the population standard deviation's common value.
As a result, pooled standard deviation is referred to as $s_p$.