Analysts say the fate of struggling internet company Yahoo Inc. likely rests on its choice of a new chief executive to replace co-founder Jerry Yang, who announced Nov. 17 that he would step down as CEO when a successor is named. But it’s not just the company’s investors who have a stake in the decision: So, too, do the millions of educators and other internet users around the world for whom web searching and related applications have assumed increasing importance.

What happens to Yahoo could determine, for instance, whether web users have a viable, powerful alternative to Google Inc. in the internet search sphere. Already, Google has garnered its share of critics who fear the search-giant’s power to control which web sites turn up first in a series of search results.

Yahoo’s fate also will decide the future of Yahoo Teachers, a peer-networking web site that aims to help instructors create, share, and modify standards-based curriculum objects. The site was announced last year but has yet to formally launch.

With Yang quitting as Yahoo’s chief executive, the company’s board of directors will confront pivotal questions as it looks for a new leader, analysts say.

Should Yahoo swallow its pride and try to strike a buyout deal with Microsoft Corp. at a price far below Microsoft’s $47.5 billion offer from six months ago? Or should Yahoo still pursue a long-awaited turnaround that’s becoming more difficult to achieve as the economy tanks?

If Yahoo plays it safe and hires someone from within or someone friendly with Microsoft, it could signal that the board merely wants an interim captain who can steer the ship until Microsoft, or possibly another buyer, comes to the rescue.

But should Yahoo recruit a CEO with a prestigious resume or pluck an up-and-coming technology star, it will be seen as a sign that the company is digging in to remain independent for the long haul.

“It’s time for Yahoo to decide if [it is] going to keep entertaining offers or really start to focus on a business strategy,” said Mike Leo, a veteran online ad executive who now runs Operative Inc. “Yahoo still has some great assets. They have just been mismanaged.”

Many analysts and investors have interpreted Yang’s departure as precursor to Microsoft’s acquisition of Yahoo in its entirety or at least its search engine.

Yahoo shares closed Nov. 20 at $8.95. That’s a fraction of the $33 per share that Microsoft offered in early May before Yang’s request for more money prompted the Redmond, Wash.-based software maker to withdraw its bid.

The negotiating breakdown infuriated shareholders, and their fury intensified as Yahoo’s stock plunged to its lowest levels since early 2003.

Yang clung to the hope that he could still engineer a comeback, but his plans went awry yet again this month when Google backed out of a proposed ad partnership to avoid an antitrust battle with the federal government.