Should "I" be used in a science fair conclusion?
Writing styles differ but using the first person singular is generally acceptable. The other option that is commonly used is to speak in passive voice or to talk about the work. You can say "I programmed Gumby to ...". You can also say "Gumby was programmed to ...". Or "The work shows that if Gumby is programmed to ...". 

There are places in which a more formal (passive voice) is preferred, but if you were in such a place you would probably already know that. Given that you ask the question, I assume you are in a more informal place, such as the US, in which using I is fine for describing your own work. 

But you might experiment a bit with how the report sounds to your own ear before deciding. You can also consult with your project advisor/instructor for advice.