There are a ton of crazy figures to digest on that page, again none addresses which sex is "swayed" more by a given advertisement. For example, "Women account for 85% of all consumer purchases including everything from autos to health care"; "Senior women age 50 and older control net worth of $19 trillion and own more than three-fourths of the nation’s financial wealth"; and "Wealthy boomer women...make 95 percent of the purchase decisions for their households".
Assuming it is true, women making 85% of consumer purchases is kind of mind blowing. This does not necessarily mean women are swayed more by marketing, but I think it is safe to say women as a whole are targeted by marketing campaigns more than men - at least after reading these numbers that is how I would market a consumer product.