TOKYO, Oct 1 (Reuters) - Japanese big manufacturers' confidence improved slightly in the three months to September, a closely watched central bank survey showed, but service-sector sentiment worsened, adding to evidence that a sales tax hike continues to weigh on the economy.

The headline index for big manufacturers' sentiment improved by 1 point from three months earlier to plus 13 in September, the Bank of Japan's quarterly "tankan" survey showed on Wednesday.

That compared with a median market forecast of plus 10.

The tankan's sentiment indexes are derived by subtracting the percentage of respondents who say conditions are poor from those who say they are good. A positive reading means optimists outnumber pessimists.

(Reporting by Leika Kihara and Tetsushi Kajimoto; Editing by Chris Gallagher)