Final Answer:
The answer of the given statement that "Elizabeth has been looking online for earrings with amethyst stones to purchase for her mother's birthday. When Elizabeth signs on to her computer at the office, there are pop-up ads for amethyst earrings on her home page. E-commerce uses to attract Elizabeth back to the site to make a purchase" is Cookies.
Explanation:
The most likely method used by e-commerce to attract Elizabeth back to the site and show pop-up ads for amethyst earrings is through the use of cookies.
Cookies are small pieces of data stored on a user's device by a web browser, and they track the user's activity on a website. This information can be used to personalize the user experience, including displaying relevant ads based on their browsing history and preferences.
While social media and data analytics information systems are also used in e-commerce, cookies are specifically designed for tracking user behavior and providing a personalized online experience, making them the most suitable option in this context.