Australian energy companies rely heavily on burning coal for electricity generation. Despite the Federal Government's decisiveness on introducing renewable energy in the country for over a decade, still there has not been a consensus between major parties on cutting the carbon emission and achieving the renewable energy target. This has led to the electricity prices being too high for everyday households and decrease in the demand for electricity. Electricity Victoria which is an electricity provider in Victoria is facing tough times with the competition and the fact that demand for electricity is on the decline. In order to encourage current and potential customers to increase their electricity usage, the company started a campaign. Management is particularly interested to know whether the mean usage after the campaign will be any different to the usage before the campaign. Previous data indicates that monthly electricity bill is normally distributed with a mean of $17.85 and a standard deviation of $3.39. The manager of the company takes a random sample of 25 household bills after running a campaign and records their monthly usage. The results show that mean usage of the sample of 25 users is $19.13. If the manager runs a hypothesis test, can he infer at the 5% significance level that the campaign was successful?

Answer all questions below.

1. State the null and alternative hypotheses.

2. State your decision rule.

3. Test your hypotheses and state your conclusion.