Grouping individuals by hash values in an array of hashes from user input and outputting names in Ruby

I have the below data structure in Ruby:

people = [
  { "name" => "John", "hobby" => "tennis", "food" => "pizza" },
  { "name" => "Joseph", "hobby" => "tennis", "food" => "burgers" },
  { "name" => "Lauren", "hobby" => "board games", "food" => "salads" } 
  { "name" => "Amir", "hobby" => "cycling", "food" => "burgers" },
  { "name" => "Mary", "hobby" => "tennis", "food" => "salads" },
  { "name" => "Karen", "hobby" => "board games", "food" => "pie" },
  { "name" => "Will", "hobby" => "cycling", "food" => "pizza" },
]

I need to write a program that will take in user input - either "hobby" or "food" and will then puts out a list of people grouped under subheadings for each hobby or food.

e.g. user inputs 'hobby' and a list is puts'ed to the console similar to the below:

tennis John Joseph Mary board games Lauren Karen cycling Amir Will

So far I have got as far as being able to generate a new array that has the hobbies and the names, however they are seperate and I'm not sure if it's the best way of going around getting the category name with a list of people underneath... also there are a few nil values being pulled out too e.g. below:

    puts "Enter what category to search"
    category = gets.chomp

    grouped_data = people.group_by { |x| x[category] }
    new_array = []
    grouped_data.each { |n| new_array.push n[0] }
    grouped_data.flatten.flatten.each { |n| new_array.push n["name"] }

    p new_array

With input "hobby" gives me an array:

    ["tennis", "board games", "cycling", nil, "John", "Joseph", "Mary", nil, "Lauren", "Karen", nil, "Amir", "Will"]

Am I on the right track? Is there another avenue worth exploring?

Thanks! Hope this has been laid out alright as it's first time posting on SA.