A. It is a premise supported by the claim that online shoppers can accomplish their task quickly with a few keystrokes and a credit card.
Incorrect. This is a premise, but it it provides the support for the popularity of online shopping. The convenience of online shopping does not explain why people loathe in person shopping.
B. It is a conclusion supported by the premise that online shopping is becoming increasingly popular.
Incorrect. This is not a conclusion. This is a statement that supports the popularity of online shopping, not the other way around.
C. It is a generalization which is based on the premise that in-person shopping takes considerably more time to accomplish than online shopping.
Incorrect. It is in a way a generalization, but it is not explicitly based on the time it takes to shop -- there are other hassles that are avoided through online shopping.
D. It is a premise given as a reason for the conclusion that online shopping is popular.
Correct. Yes, it s a premise. "People loathe online shopping" can directly explain "online shopping is popular."
E.It is a conclusion supported by evidence of the hassles of in-person shopping in comparison to online shopping.
Incorrect. While it is supported by the comparison between in-person and online shopping, it does not play the role of the conclusion in this paragraph.