How to change the amount of posts previewed on a page?

You’re missing an s.

$query->set('posts_per_page', '1');

However – you probably don’t want to do this for every query, since that affects everything – widgets, back end, everything. You should make it conditional. For example:

<?php
function university_adjust_queries($query) {
    // If this is the main query, not in wp-admin, and this is the homepage
    if($query->is_main_query() && !is_admin() && $query->is_home()) {
        $query->set('posts_per_page', '1');
    }
}
add_action('pre_get_posts', 'university_adjust_queries');
?>

This will make sure you’re only affecting the main query (The Loop) on the homepage, and only on the front end. You can adjust the condition to target whichever spot you’re wanting to affect.