Choose the correct form of tense for the given sentence:
According to researchers, our sleep time over the past century ______ by about 20 percent.

In the given sentence we are talking about the data which is already covered so we use present perfect tense here i.e. 'has reduced' will come.
Present perfect tense combines the present tense and the perfect aspect used to express an event that happened in the past that has present consequences. The present perfect is used to indicate a link between the present and the past.
Example: I have just finished my work.
Hence the correct sentence is:
According to researchers, our sleep time over the past century has reduced by about 20 percent.