Final answer:
The statement is false; the number of slaves in the South grew mainly due to the cotton boom, but the actual proportion of white families owning slaves did not increase as significantly as suggested.
Step-by-step explanation:
The statement that between the years 1830 and 1860 the proportion of southern white families who held slaves increased from one in four to one in three is false. During this period, the South's enslaved population grew dramatically, primarily due to the domestic slave trade and the economic boom brought on by cotton, exemplified by Eli Whitney's invention of the cotton gin. However, the proportion of white families owning slaves did not increase as dramatically as the question suggests, mainly because the wealth and slaves were concentrated among a relatively small segment of the population. Instead, slavery became more entrenched in the Deep South due to the larger plantations and the greater demand for slave labor in these areas. While the total number of slaves increased, the actual proportion of white families that owned slaves did not rise in the way the question states.