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

In the past, the mean price was $1.65 a litre.

Recently, a random sample of 25 petrol stations had a mean petrol price of $1.70 with a standard deviation of $0.05.

Assume the distribution of unleaded petrol prices is normal.

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%.

State your decision.

State your conclusion.