A consumer group claims that the price of unleaded petrol is increasing.

In the past, the mean price was $1.35 a litre.

Recently, a random sample of 36 petrol stations had a mean petrol price of $1.75 with a standard deviation of $0.08.

What are the null and alternative hypotheses to test the consumer group's claim?

Show basic workings to give the value of the calculated test statistic.

Give the critical value if testing at of 1%.