Australians are so ignorant about the carbon tax that more than half think it has pushed up the price of petrol.

Nine months after its introduction 54 per cent of people believed the tax, which specifically excludes motor fuel, had pushed up prices at service stations. Most people surveyed also estimated that their cost of living had risen by $20 or more a week, while 5 per cent put the increase at more than $100 a week.

The government's modelling came up with $9.90 a week.

Asked about compensation, 49 per cent said they had received nothing at all, whereas the compensation package introduced with the tax applies to 90 per cent of the population.