What is the difference between pooled cross sectional data and panel data?

Pooled Cross Sectional Data are obtained by collecting random samples from a large polulation independently of each other at different points in time.

Panel Data consists of time series for each statistical unit in the cross section. Its like randomly selecting our cross section only once, and then following each statistical unit within this cross section over time. Thus all cross sections are equally large and consist of the same statistical units

T-test is used to estimate population parameter and hypothesis testing for population mean. 

F-test is used to test any variance in population parameters. F-test is the ratio of variance of two samples.