"iie. mimasen deshita" not "iie. eiga wo mimasen deshita" ???
I am doing some exercises in my workbook and the question is:

Mari-san wa ketsuyoobi ni eiga wo mimashitaka

The answer is: iie. mimasendeshita (she actually wrote a letter)

Would it be wrong to use 'iie. eiga wo mimasendeshita' as this sounds more natural to me?

I have heard a lot of 'inferred' information can be dropped from sentences in Japanese, is this an example of this?

Any info gratefully received :), and apologies for the romaji formatting, I don't read much romaji to know how to split the words well.

Question

"iie. mimasen deshita" not "iie. eiga wo mimasen deshita" ???
I am doing some exercises in my workbook and the question is:

Mari-san wa ketsuyoobi ni eiga wo mimashitaka

The answer is: iie. mimasendeshita  (she actually wrote a letter)

Would it be wrong to use 'iie. eiga wo mimasendeshita' as this sounds more natural to me?

I have heard a lot of 'inferred' information can be dropped from sentences in Japanese, is this an example of this?

Any info gratefully received :), and apologies for the romaji formatting, I don't read much romaji to know how to split the words well.

Answer

Yup! The answer should be: いいえ、みませんでした。
It's just similar to English, when you ask someone: Did you watch the movie last night? 
Normally, the answer will be: Yes, I did/No, I didn't. (Not: Yes, I watched the movie/No, I didn't watch the movie; except in case you wanna emphasize or give additional information).