I'd go for, "the". It is "The majority" as opposed to, "The minority", The sentence means they are looking to focus spending money on advertising, and they want to find out where women spend the majority of their time, so they can get their attention with advertising. "A majority of their time" - "it's true that women IN GENERAL spend a majority of their time, looking at clothes online". "Women in the 18-50 age range spend THE majority of their time ONLINE, looking at clothes." "A" is to be used when something is spoken about in general terms, "the" is to be used when you know the facts. You can't really have, "a majority" though - having a majority and using it as a fact or figure, is a statistic, so I'd say if you are presenting a factual statement, use "the majority". "sh*t or get off the pot" as they say :D (sh*t - is a vulgarity).

SCRIPT Boss: "Okay, Scavo, you're up. Let's here this genius idea of yours." Tom: "Okay. Uh, okay. The single greatest obstacle facing Spotless Scrub is a lack of visibility. We need to concentrate ad spending in places where women spend THE majority of their time the = definite article a/an = indefinite article The is used to refer to a specific or particular member of a group. For example, "I just saw the most popular movie of the year." There are many movies, but only one particular movie is the most popular. Therefore, we use the. "A/an" is used to refer to a non-specific or non-particular member of the group. For example, "I would like to go see a movie." Here, we're not talking about a specific movie. We're talking about any movie. There are many movies, and I want to see any movie. I don't have a specific one in mind. THE: "The dog that bit me ran away." Here, we're talking about a specific dog, the dog that bit me. "I was happy to see the policeman who saved my cat!" Here, we're talking about a particular policeman. Even if we don't know the policeman's name, it's still a particular policeman because it is the one who saved the cat. "I saw the elephant at the zoo." Here, we're talking about a specific noun. Probably there is only one elephant at the zoo. A/AN: "My daughter really wants a dog for Christmas." This refers to any dog. We don't know which dog because we haven't found the dog yet. "Somebody call a policeman!" This refers to any policeman. We don't need a specific policeman; we need any policeman who is available. "When I was at the zoo, I saw an elephant!" Here, we're talking about a single, non-specific thing, in this case an elephant. There are probably several elephants at the zoo, but there's only one we're talking about here.

Only one majority can exist, so "the" is correct. People do commonly say "a majority", but it is not correct to do so.

where women spend THE majority of their time. There can not be more than one majority ..... In any space of time, in any volume of substance, in any countable objects, in any measurement, there is only one section that can be the majority. There cannot be two majorities. God job!