An electricity company wants to look to see if installing a smart meter where people can track their electricity usage throughout the day changes the way that people use electricity. Past information suggests that the average household uses 2.05 of electricity per day. After installation the average household uses 2.01 per day based on a sample of 200 households and the data shows a standard deviation on 0.23.

Did the installation of the smart meter have an effect on the electricity usage? Establish null and alternative hypotheses and using a z-test, test the hypothesis at a 2% significance level.

Please include working out.