English that can often be dropped from a sentence.
(1) I think (that) she can come.
(2) I don't think (that) she can come.
In some negative constructions, complementiser dropping sounds marked.
A: Does Alex go to dance practice on Wednesdays?
(4) B: I know that he goes Fridays, but I don't know that he goes Wednesdays.
(5) B: *I know he goes Fridays, but I don't know he goes Wednesdays.
(6) I don't know that I can finish the report by next week...
(7) *I don't know I can finish the report by next week.
Some native speakers have told me that even (4) and (6) are a bit marked, and that they would have if or whether there, which would explain why (7) is unacceptable, as neither of those can be dropped. Gewgle has lots of examples of 'I don't know that I can do it', so it's definitely an attested construction even if it's not prescriptively grammatical. The examples below were accepted as grammatical by the native speakers I consulted, but all had the sense that they would say (10) more easily than (9).
(8) I hope (that) she kills them.
A: Are you seriously hoping to see bloodshed at your daughter's soccer match?
(9) B: I don't hope she kills them(, but a little bit of carnage might be nice).
(10) B: I don't hope that she kills them(, but a little bit of carnage might be nice).
Does anyone know of any reason why complementiser dropping would be rarer in negative contexts? Or are my three native speakers simply not representative?